Answer two questions about Systems AAA and BBB:
System AAA \text{\quad}start text, end text System BBB
\begin{cases}6x-5y=1\\\\-2x+2y=-1\end{cases}









6x−5y=1
−2x+2y=−1

\begin{cases}4x-3y=0\\\\-2x+2y=-1\end{cases}









4x−3y=0
−2x+2y=−1

1) How can we get System BBB from System AAA?
Choose 1 answer:

(Choice A, Checked, Correct)
CORRECT (SELECTED)
Replace one equation with the sum/difference of both equations

(Choice B, Incorrect)
INCORRECT
Replace only the left-hand side of one equation with the sum/difference of the left-hand sides of both equations

(Choice C, Incorrect)
INCORRECT
Replace one equation with a multiple of itself

2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution?
CORRECT (SELECTED)
Yes

Answers

Answer 1

For the given systems A and B:

1) Replace the first equation of A by the sum between the two equations of A.

2) Yes, the systems are equivalent.

How to get system B from system A?

Here we have the two systems of equations:

A:

6x - 5y = 1

-2x + 2y = -1

B:

4x - 3y = 0

-2x + 2y = -1

The second equation is the same in both systems, so we only look at the first equations.

In A we have:

6x - 5y = 1

If we add the second equation of A, then we get:

(6x - 5y) + (-2x + 2y) = 1 + (-1)

4x - 3y = 0

This is the first equation of B.

Then we need to replace the first equation by the sum between the first and second equations.

2) Are the systems equivalent?

Yes, because we did not "modify" system A, we just rewrite it and we got system B, then both systems have the same solutions.

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Answer 2

Answer: A) , Yes

Step-by-step explanation:


Related Questions

Please help me....trying to get my HS diploma, i did not graduate :(
A ball is thrown in air and it's height, h(t) in feet, at any time, t in seconds, is represented by the equation h(t)=−t2+7t. When is the ball higher than 10 feet off the ground?

Answers

Answer:

A.

Step-by-step explanation:

so, the equation is

h(t) = -t² + 7t

so, we need to find the solutions for t (the time when the ball is exactly 10 ft in the air). there had to be 2 solutions, as the ball first goes up passing the 10 ft height, and then comes back down again, passing the 10 ft mark a second time. and between these 2 times the ball is higher (but not equal, so, we can only use < or > as inequality signs) than 10 ft.

10 = -t² + 7t

-t² + 7t - 10 = 0

the generation solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = t

a = -1

b = 7

c = -10

t = (-7 ± sqrt(7² - 4×-1×-10))/(2×-1) =

= (-7 ± sqrt(49 - 40))/-2 = (-7 ± sqrt(9))/-2

t1 = (-7 + 3)/-2 = -4/-2 = 2 seconds

t2 = (-7 - 3)/-2 = -10/-2 = 5 seconds

so, between 2 and 5 seconds airtime the ball is higher than 10 ft.

and remember : HIGHER THAN.

so, we cannot use any equality (like <= or >=).

t must be higher than 2 and lower than 5 :

2 < t < 5

Find the measure of the exterior 1.

A. 11°
OB. 127°
O C. 85°
O D. 95°

Answers

Answer: D) 95°

Step-by-Step Solution:

We know that the Exterior Angle of a Triangle = Sum of Opposite Interior Angles of the Triangle.

Therefore,

∠1 = 53° + 42°
=> ∠1 = 95°

Hence, ∠1 = 95°

solving 3 x plus 8 equals 14

Answers

Answer x= 2
3x + 8 = 14
To solve subtract 8 from both sides to isolate x
3x = 6
Now divide both sides by 3 to solve for x
X = 2

3x + 8 = 14, this would equal 2, 3(2) = 6, 6 + 8 = 14, therefore the answer is x = 2.

Solve algebraically
X+4=-2

Answers

Answer:

x=-6

Step-by-step explanation:

-6+4=-2
Give brainliest please

1/12^-2 using positive exponents​

Answers

SOLVING

[tex]\Large\Box\underline{\textsf{A. What is Asked}}[/tex]

Evaluate [tex]\bf{\dfrac{1}{12^{-2}}}[/tex]

[tex]\Large\Box\underline{\textsf{B. This problem has been solved!}}[/tex]

[tex]\boxed{\begin{minipage}{9cm} \text{If we have negative exponents in the denominator} \\ \text{we turn over the number,} \\ \text{leaving positive exponents only.} \end{minipage}}[/tex]

Thus,

[tex]\bf{\dfrac{1}{12^{-2}}=\dfrac{12^2}{1}}[/tex]. | see, the negative exponent turned into a positive one as soon as the fraction was turned over.

[tex]\bf{144}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

             [tex]\bf{=144}[/tex]

Extra information [tex]\curvearrowright[/tex]

      [tex]\begin{tabular}{c | 1} Expression & Exponent Rule\\\cline{1-2} \\ x^m*x^n & add the powers \\ x^m\div x^n & subtract the powers \\(x^m)^n & multiply the powers \\ x^{-m} & turn over the number \\ x^0 & this equals one\end{tabular}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]

Help me please T^T

Solve for m.
m+1/3<-2 1/4

Answers

Answer:

answer is the second option  m<-2 7/12

Step-by-step explanation:

process:

convert -2 1/4 into an improper fraction

m+1/3 < -9/4

m <-9/4 -1/3

calculate the difference

m<-31/12

turn into a mixed fraction

Two gymnasts are running toward each other in a floor routine, and they plan to precisely time a flip to stay synchronized for the audience. The path of the gymnasts is parabolic and modeled by the following equations, where y is the height of the flip and x is the time in seconds.
= – (x – 5)2 + 3
y = –3(x –6)2 + x + 1
2seconds
3seconds
4seconds
5seconds

Answers

To make sure the flip is in unison after 4  seconds should the flip occur, as given by option C: 4 seconds.

We have given that,

Two gymnasts are running toward each other in a floor routine, and they plan to precisely time a flip to stay synchronized for the audience.

What does synchronized motion mean?

Synchronized motion is a motion of two or more system which goes in synchronization with each other.

For this case, the flip will occur such that both gymnasts are synchronized and the flip is in unison (simultaneous).

For that, we need the time(x) and the height (y) same.

Since the motion paths are:

[tex]y=-(x-5)^2+3[/tex]

[tex]y=-3(x-3)^2+x+1[/tex]

Therefore, we need to find the values of x for which the same y comes as output.

Let x =  t be the time for which the height y is the same, then:

[tex]-(t-5)^2+3=-3(t-3)^2+t+1[/tex] = height achieved by both gymnasts.

Solving it further:

[tex]-(t-5)^2+3=-3(t-3)^2+t+1[/tex]

t=4,t=1/2

Assuming they planned to do a flip after an integral number of time in seconds, the correct option is t = 4 seconds.

Thus, to make sure the flip is in unison after 4  seconds should the flip occur, as given by the option C: 4 seconds.

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Kate is the captain of a large cruise ship. As she

drives the ship, she sits 50 meters above the sea.

Paul is the captain of a boat. He sits 15 meters

above the sea. If the radius of the earth is

6,371,000 meters, how much further can Kate see

across the horizon than Paul?



here are the first few questions the rest are in the picture.


1.Show me that you understand the problem. restate it in your own words and identify the important information.


2. what is your prior knowledge and what tools do you have to solve this problem?

a. Draw two diagrams, one for Kate and one for Paul. Include important numbers. Insert your diagrams into your answer.

Answers

The amount further by which Kate can see across the horizon than Paul is; 3.33 times farther

How to use volume of a cone in applications?

Formula for volume of a cone is;

V = ¹/₃πr²h

For Kate:

Height (h) = 50 m

Radius (r) = 6,371,000 m

Thus;

V = ¹/₃ * π * (6,371,000)² * 50

V = 2.12526863 × 10¹⁵ m³

To determine how much further can kate see across the horizon than Paul, we have:

⇒ (2.12526863 × 10¹⁵ m³)/6.3758059 × 10¹⁴ m³

= 3.33 times further.

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A $15 credit to revenue was posted as a $150 credit by what amount is the revenue account in error?

Answers

Answer: Multiple Choice $15 understated. $135 overstated. $135 understated. $150 understated. $150 overstated. 2.The numbering system used in a company's chart of accounts: Typically begins with income statement accounts.

Step-by-step explanation:

Solve linear equations using substitution y=-4x
y=4x+16

Answers

Answer:

(-2 , 8)

Step-by-step explanation:

[tex]\begin{cases}y=-4x&\\ y=4x+16&\end{cases}[/tex]

We substitute y by -4x in the second equation of the system:

-4x = 4x + 16

⇔ -8x = 16

⇔ x = 16/(-8)

⇔ x = -2

Now ,we substitute x by -2 in the first equation of the system:

y = -4 × (-2) = 8

then

the solution of the system is {(x = -2 , y = 8)}

Another geometry question thanks!

Answers

For the given right triangle, we have:

L = 57°ML = 4.5NL  =  7.5How to get the dimensions of the given triangle?

Here we have a right triangle, remember that the sum of the internal angles of a triangle must be 180°, then:

N + M + L = 180°

We can see that:

N = 37°

M = 90°

Then:

L = 180° - N - M = 180° - 37° - 90° = 53°

Also, if we step on N, the adjacent cathetus measures 6 units, then we can use the relations:

tan(37°) = (opposite cathetus)/(adjacent cathetus)

tan(37°) = ML/6

tan(37°)*6 = ML = 4.5

cos(37°) = (adjacent cathetus)/(hypotenuse)

cos(37°) = 6/NL

NL = 6/cos(37°) =  7.5

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Suppose that the functions and are defined as follows. p(x)=-x and q(x)=2x^2-2
find the following (q°p)(2)=
and (p°q)(2)=

Answers

The two compositions for the functions are:

[tex](p\°q)(2) = -6\\\\(q\°p)(2) = 6[/tex]

How to get the compositions?

When we have two functions q(x) and p(x), the composition is:

[tex](q\°p)(x) = q(p(x))[/tex]

Here we have:

[tex]p(x) = -x\\\\q(x) = 2x^2 - 2[/tex]

The first composition is:

[tex](q\°p)(2) = q(p(2)) = 2*(p(2))^2 - 2 = 2*(-2)^2 - 2 = 6[/tex]

The other composition is:

[tex](p\°q)(2) = p(q(2)) = -(q(2)) = -(2*2^2 - 2) = -(8 - 2) = -6[/tex]

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(1.5 x 10^8) + ( 2.06 x 10^8) =

Answers


(1.4x10^8) + (2.06x10^8)=

356,000,000

Answer:

356000000

Step-by-step explanation:

1. Simplify the expression

Calculate the expression inside the parentheses.

[tex](1.5*10^8)+(2.06*10^8)[/tex]

Simplify exponents and square roots

[tex](1.5*10^8)+(2.06*10^8)[/tex]

[tex](1.5*100000000)+(2.06*10^8)[/tex]

Perform any multiplication or division, from left to right:

[tex](1.5*100000000)+(2.06*10^8)\\[/tex]

[tex](150000000)+(2.06*10^8)[/tex]

Simplify exponents and square roots

[tex]150000000+(2.06*10^8)[/tex]

[tex]150000000+(2.06*100000000)[/tex]

Perform any multiplication or division, from left to right:

[tex]150000000+(2.06*100000000)[/tex]

[tex]150000000+(206000000)[/tex]

Calculate any addition or subtraction, from left to right.

[tex]150000000+206000000[/tex]

[tex]356000000[/tex]

Why learn this

Order of operations is a basic rule of algebra. It tells us what to solve first when we have an equation with multiple functions, which is something that you will likely encounter throughout your maths studies. The order is: Parentheses, Exponents, Multiplication and Division, then finally Addition and Subtraction. Remember that when you're solving within the parentheses, the Order of Operations applies!

Terms and topics

Order of operations

Scientists want to test a new pair of running shoes. A speed test is performed with two separate groups of participants. The treatment group will wear the new pair of running shoes, while the control group will not. It is believed that age and height may affect speed. Which of the following would be most effective in controlling the confounding variables, such as age and height, in this study?

Answers

The most effective in controlling the confounding variables is matched pairs design.

What is a matched pair design experiment?

A matched pairs design is when participants are matched based on shared characteristics that is of importance to the experiment. One member of the pair is put in the control group while the other is put in the experimental group.

Here are the options:

A completely randomized design experiment

A longitudinal observational study

A retrospective observational study

A matched-pair design experiment

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Chana and Josiah started skating at the same time in the same direction, but Josiah had a head start 10 meters past the starting line. Chana skated 3 meters per second and Josiah skated 2 meters per second.

What does point I represent in this context?

CORRECT (SELECTED)
Chana's distance from the starting line at a time when she is behind Josiah

Answers

The point that is labeled H on this graph is that at 25th second, Josiah is 60 meter distance from the starting line.

What is the distance about?

Note that At the point H, there is  found to be an intersection between the distance taken by both people involve so:

Y (a)= 10 + 2x ------ Josiah

Y (0) = 3x   ----- Chana

If  Y (a)= Y (0)

Then:

10 + 2x = 3x

x = 10

F = x = 20

Y (o) = 60

If x = 20

= then Y(0) = 3 x 20

= 60

Therefore, The point that is labeled H on this graph is that at 25th second, Josiah is 60 meter distance from the starting line.

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Transcribed image text: In 2000, 47% of the residents in a large city regularly used newspapers for getting news and this has decreased at an average rate of approximately 1.8% per year since then. Find a linear function in slope-intercept form that models this description. The function should model the percentage of residents, P(x), who regularly used the news outlet x years after 2000 P(x)= (Use integers or decimals for any numbers in the expression.)

Answers

Answer:

/.............................../././///////////////////////////////////////

Step-by-step explanation:

.

Assume that the random variable X is normally distributed with mean y = 60 and standard deviation a = 12. Find the 87th percentile for X

Answers

The 87th percentile is the value [tex]x_{0.87}[/tex] such that 87% of the distribution lies below [tex]X=x_{0.87}[/tex], i.e.

[tex]P(X \le x_{0.87}) = 0.87[/tex]

Transform [tex]X[/tex] to the standard normal random variable [tex]Z[/tex], then solve for [tex]x_{0.87}[/tex] using the inverse CDF of [tex]Z[/tex].

[tex]P(X\le x_{0.87}) = P\left(\dfrac{X-60}{12} \le \dfrac{x_{0.87}-60}{12}\right) = P\left(Z \le \dfrac{x_{0.87}-60}{12}\right) = 0.87[/tex]

[tex]\implies \dfrac{x_{0.87}-60}{12} = F_Z^{-1}(0.87) \approx 1.12369[/tex]

[tex]\implies \boxed{x_{0.87} \approx 73.5167}[/tex]

What is the sum of the first 20 terms of the arithmetic sequence 3,9,15,21,27

Answers

Answer: 6

Step-by-step explanation: 3 + 6 = 9,  9 + 6 = 15,  15 + 6 = 21,  21 + 6 = 27

x, 3x and 5x ,find the sum

Answers

x + 3x + 5x ( the variables are same you can add them immediately )

9x ( the answer is 9x for adding terms with the same variable just add the numbers and write the variable as itself)

HOPE IT HELPS

Answer: 9x

Step-by-step explanation:

As the variables are of same power (1) we can add it

x+3x+5x=9x

what is the z score of x=12 if it is two standard deviations to the right of the mean?

Answers

The value of the Z-score will be equal to 2.

What is Z-score?

The z score indicates how many standard deviations your score is from the mean.

At the mean position, the standard deviation is 0 now the z score is the measure of the data which is how far from the mean. So the given data is at two standard deviations to the right of the mean so the Z-Score will be 2.

Therefore the value of the Z-score will be equal to 2.

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point O, A, B lie on the same line. OA=12cm and OB=9cm. find the distance between the midpoints of segments OA and AB in each case

Answers

The Distance  between the midpoints of segments OA and AB is 4.5cm

Lines and measures

A line is defined as the shortest distance between two points.

Given the following parameters

OA = 12cm

OB = 9cm

AB = OA - OB

AB = 12 - 9 = 3cm

midpoint of OA = 12/2 = 6cm

midpoint of AB = 3/2 = 1.5cm

Distance  between the midpoints of segments OA and AB in each case will be the difference between the midpoints

Difference = 6cm - 1.5

Difference = 4.5cm

Hence the Distance  between the midpoints of segments OA and AB is 4.5cm

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Billy received a raise after his first year on the job to $45,000 from his initial salary of $42,400. What was his real raise stated as a percentage? Inflation averaged 2.4 percent for the year. Round your answer to two decimal places.

Answers

Billy get 5.9% raise after completing first year.

What is PERCENTAGE?

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.

Here, Billy's initial salary = $ 42,500

After raise, salary become $ 45,000

Change in salary = Raised salary - Initial salary

                            = 45000 - 42500

                            = $ 2500

% Change = change / initial salary  X 100

                  = 2500 / 42500 X 100

                  = 0.0589 X 100

                  ≈ 5.9 %

Thus, Billy get 5.9% raise after completing first year.

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The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is four
times the measure of the first angle. The third angle is 12 more than the second. Let x, y, and z represent the measures of
the first, second, and third angles, respectively. Find the measures of the three angles.

Answers

Answer:

x = 36°

y = 66°

z = 78°

Step-by-step explanation:

General outline:Setup equations for each sentenceSolve the resulting system

Setup equations:

Allowing the first angle to be x, the second to be y, and the third to be z, the three sentences describing the relationships between angle measures are given below:

Eq1:  x + y + z = 180°Eq2:  y + z = 4xEq3:  z = y + 12°

Solve the system

Substituting equation 3, into equations 1 and 2

Eq1:  x + y + z = 180°

x + y + (y+12°) = 180°

x + 2y + 12° = 180°

x + 2y = 168°

x = 168° - 2y

Eq2:  y + z = 4x

substituting the result from equation 1, and Equation 3...

y + (y+12°) = 4*(168° - 2y)

2y + 12° = 672° - 8y

10y = 660°

y = 66°

Substituting back into Equation 3...

Eq3:  z = y + 12°

z = (66°) + 12°

z = 78°

Substituting both y, and z into Equation 1...

x + y + z = 180°

x + (66°) + (78°) = 180°

x + 144° = 180°

x = 36°

So, the three angle measures are:

x = 36°

y = 66°

z = 78°

Verification

"The sum of the measures of the angles of a triangle is 180."

x + y + z = 180°

36° + 66° + 78° = 180°

True

"The sum of the measures of the second and third angles is four times the measure of the first angle"

y + z = 4x

66° + 78° = 4*(36°)

144° = 144°

True

"The third angle is 12 more than the second"

z = y + 12°

78° = 66° + 12°

True

Factorize x^2+√4x+2x+2
[tex]factorize \: {x}^{2} + \sqrt{4x} + 2x + 2 [/tex]

Answers

Answer:

x^2+4x+2

Step-by-step explanation:

√4 = 2

=x^2+2x+2x+2

add the ones that are the same (2x+2x)

x^2+4x+2


Question 9
The pOH of a solution is 5.70.
What is its hydroxide-ion concentration?
O 3.3 × 10-3
2.8 × 10-9
2.5 x 10-7
2.0 x 10-6
C

Answers

The pOH of a solution is 5.70. The correct option is C; 2.5 x 10-7 is the hydroxide ion concentration.

What is the pOH of the solution?

The pOH of the solution is the negative logarithm of hydroxide ions concentration in a solution. The lower the value of pOH more alkaline will be the solution.

Mathematically written as:

pOH = - Log[OH-]

The sum of ph and pOH is equal to 14.

pH + pOH = 14

The pOH of a solution is 5.70.

pOH = - Log[OH-]

5.70 =  - Log[OH-]

[OH-] = 2.5 x 10-7 is the hydroxide ion concentration.

The solution has a pH value of more than 7 which means that it is base.

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10) Choose the solution for each linear system.
(3,0)
(-3,-1)
(2,-1)
(-2,1)
(x-2y=4
4x + 2y = 6
11) Choose the solution for each linear system.
(2,4)
O(-2,-4)
O (4,2)
O(-4,-2)
[6x-2y = -4
-4x+3y=-4

Answers

Answer:

10.  C. (2, -1)11.  B. (-2, -4)

Step-by-step explanation:

10.

[tex]\left \{ {{x-2y=4} \atop {4x+2y+6}} \right.[/tex]

The y values cancel out if you add the equations

5x = 10

x = 2

plug in x

2 - 2y = 4

-2y = 2

y=-1

Answer: C. (2, -1)

11.

[tex]\left \{ {{6x-2y=-4} \atop {-4x+3y=-4}} \right.[/tex]

In order to get terms to cancel out, multiply the top by 3 and bottom by 2

[tex]\left \{ {{18x-6y=-12} \atop {-8x+6y=-8}} \right.[/tex]

The y values cancel out if you add the equations

10x = -20

x = -2

plug in x

6(-2) - 2y = -4

-12 - 2y = -4

-2y = 8

y = -4

Answer: B. (-2, -4)

Natasha had a $922.93 balance on her credit card at the beginning of September. Her credit card has an APR of 9.89%, compounded monthly, and a minimum monthly payment of 3.08% of the total balance. The following table shows Natasha’s credit card purchases over the next two months.
Month
Cost ($)
September
33.70
October
61.70
October
27.80
If Natasha makes only the minimum payments, what will her balance at the beginning of November? (Assume that the interest accrues before the monthly payment, and that the monthly payment occurs at the end of the month. Round all dollar values to the nearest cent.)

Answers

Answer:

Her balance at the beginning of November=$973.76

Step-by-step explanation:

What is Natasha's credit balance at the beginning of November?(i.e. at the end of October)

The balance at the end of each month is the beginning balance plus the current month's purchases minus the minimum payment for the month.

Sept =$922.93+$33.70+9.89%/12*($922.93+$33.70)

Sept=$964.51

payment= 964.51*3.08%

balance at the end of Sept=$964.51-($964.51*3.08%)

balance at the end of Sept=$934.80

Oct=$934.80+$61.70+9.89%/12*($934.80+$61.70)

Oct=$ 1,004.71

payment=$1,004.71*3.08%

balance at the end of Oct(at beginning of Nov)=$ 1,004.71-($1,004.71*3.08%)

balance at the end of Oct(at beginning of Nov)=$973.76

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Answer:

The answer is C.$1,000.93 just did it om edge

Step-by-step explanation:

Solve the following system by the substitution method. Check the solution(s)
7x + 4y = 10
x+y=1

Answers

Answer:

x = 2; y = -1

Step-by-step explanation:

We can solve (first for y, then for x) using substitution:

[tex]x+y=1\\7x+4y=10\\(x+y=1)-y\\x=1-y\\\\7(1-y)+4y=10\\7-7y+4y=10\\(7-3y=10)-7\\(-3y=3)/-3\\y=-1\\\\(x-1=1)+1\\x=2[/tex]

A number generator was used to simulate the percentage of people in a town who join a health club yearly. The process simulates randomly selecting 100 people from the town and was repeated 20 times. The percentage of people who join a health club yearly is shown in the dot plot. Which statement is most likely true about the population of the town? Most likely, 50% of the people in the town join a health club yearly. Most likely, about 40% to 60% of the people in the town 0 10 20 acer 30 40 50 60 70 80 : 90 100 A number generator was used to simulate the percentage of people in a town who join a health club yearly . The process simulates randomly selecting 100 people from the town and was repeated 20 times . The percentage of people who join a health club yearly is shown in the dot plot . Which statement is most likely true about the population of the town ? Most likely , 50 % of the people in the town join a health club yearly . Most likely , about 40 % to 60 % of the people in the town 0 10 20 acer 30 40 50 60 70 80 : 90 100​

Answers

The statement that's is likey true about the population of the town is that most likely about 40% to 60% of the people Jon the health club yearly.

How to illustrate the information?

It should be noted that a dot plot simply gives a pictorial representation of the information given.

In this case, the population of the town is that most likely about 40% to 60% of the people Jon the health club yearly.

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Answer: Most likely, about 40% to 60 % of the people in the town join a health club yearly.

Step-by-step explanation:

I need the correct answer for questions 1 ​

Answers

The truth values of the propositions are false, true and false

How to determine the true values?

The Boolean variables are given as:

p = false

r = false

q = true

s = true

The truth values of the propositions are as follows:

1. (s → (p ∧ ¬ r)) ∧ ((p → (r ∨ q)) ∧ s)

As a general rule:

∧ means and

¬ not

∨ or

So, we have:

(true → (false ∧ ¬ false)) ∧ ((false → (false ∨ true)) ∧ true)

¬ false= true.

So, we have:

(true → (false ∧ true)) ∧ ((false → (false ∨ true)) ∧ true)

false ∧ true = false and false ∨ true = true

So, we have:

(true → false) ∧ ((false → true) ∧ true)

false → true = true and true → false = false

So, we have:

(false) ∧ (true ∧ true)

true ∧ true = true

So, we have:

false ∧ true

Lastly

false ∧ true = false

Hence, the truth value of (s → (p ∧ ¬ r)) ∧ ((p → (r ∨ q)) ∧ s) is false

2. ((p ∧ ¬ q) → (q ∧  r)) → (s ∨ ¬q)

This means

((false ∧ ¬ true) → (true ∧  false)) → (true ∨ ¬true)

Using the established rules in (1), we have:

((false ∧ false) → (true ∧  false)) → (true ∨ false)

This gives

((false → false)) → true

This gives

true → true

Lastly, we have:

true

Hence, the truth value of ((false ∧ ¬ true) → (true ∧  false)) → (true ∨ ¬true) is true

3. (p → q) ∧ (q → r)

This gives

(false → true) ∧ (true → false)

Using the established rules in (1), we have:

true ∧ false

This gives

false

Hence, the truth value of (p → q) ∧ (q → r) is false

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