Use the rules of inference to prove the conclusion r given (all 1,2,3 and 4) the four premises listed below. Write your solution as a numbered sequence of statements. Identify each statement as either a premise, or a conclusion that follows according to a rule of inference from previous statements, or it is equivalent to a previous statement by the rules of logical equivalences. You should give the rule used by name and refer by number to the previous statement(s) that the rule was applied to.
a. p +- (premise)
b. p Vu (premise)
c. q (premise)
d. ((r Λ t) V p) V-u (premise)
Answers
Answer:
attached below
Step-by-step explanation:
Applying the rule of logical equivalences
attached below is a detailed solution ( written as a numbered sequence of statements )
Answer:
identity laws, domination laws, commutative laws, double negation laws these are some laws from logical equivalence.
What is logical equivalence?
A tautology is a claim that is true no matter what the truth values of the propositional variables it includes are.Contradictions and absurdities refer to a group of propositions that are all untrue.It's also known as a contingency when a composite proposition contains neither a tautology nor a contradiction.What does this imply in actuality, though?To make sense of this, go to the following truth table.
Contradiction and tautology
Inconsistency, contradiction, and tautology So a tautology is when every single statement in a column is true, as defined by Oak Ridge National Laboratory, and is often indicated by a bold-faced capital T. When the entire column is untrue, a contradiction, which is often denoted by a boldface capital F, exists.
However, why is this significant?
We may better understand propositional equivalences, or assertions that are equivalent in logical reasoning, by using tautologies and contradictions, which are necessary in establishing or verifying mathematical arguments. Our task will be to confirm the logical equivalentity of propositions like p and q.
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Related Questions
A map is drawn to scale such that 1 inch equals 100 miles. To mark a distance of 500 miles, the length on the map must be_____ inches.
Answers
Answer:
5 inches
Step-by-step explanation:
its simple
1in-100m
500m= 100m x 5
so multiply five to the other side
1in x 5=5 in
5in-500m
Answer:
5 inches
Step-by-step explanation:
100 miles = 1 inch
500 miles = 500/100 * 1 = 5 inches
you're welcome....
I need help with these 2 questions!! please 20 points!!!
Answers
9514 1404 393
Answer:
45 cm²38 cm²Step-by-step explanation:
The conventional way to work these problems is to make use of the formulas for areas of a triangle, rectangle, and semicircle. If you've used these formulas for a while, you recognize that they give you certain relationships that may make these problems easy to do mentally.
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1. The area of a triangle is half the product of height and width, so is equivalent to the area of a rectangle either half as high, or half as wide. We note that the width of the sail is 5 cm, so half that is 2.5 cm--exactly the same as the height of the boat's hull. That means we can add the height of the sail to the length of the boat, and the total area can be considered to be the same as that of a rectangle that is
2.5 cm high × (12 cm + 6 cm) long = (2.5)(18) cm² = 45 cm²
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2. The usual formula for the area of a circle is ...
A = πr²
When expressed in terms of diameter, this becomes ...
A = π(d/2)² = (π/4)d²
Then the area of a semicircle is half that, or (π/8)d². This is equivalent to the area of a rectangle that is "d" wide and "π/8·d" high. That is, the approximate area of the semicircle is that of a rectangle 4 cm high by (π/8·4 cm) = π/2 cm wide. In other words, the semicircle effectively adds π/2 cm to the left end of the 6 cm central rectangle of the figure.
As discussed above, the area of a triangle is equivalent to the area of a rectangle half as high. In this figure, the triangle is 10-6 = 4 cm wide, so can be considered to contribute 4/2 = 2 cm to the right end of the 6 cm central rectangle.
If we consider π ≈ 3, then the approximate area of the figure is ...
(4 cm)(3/2 cm + 6 cm + 2 cm) = (4)(9.5) cm² = 38 cm²
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The exact value is 4(8+π/2) = 32+2π ≈ 38.283 cm².
If f4y 3 = 6y + 9, what is the value of 7y?
Answers
Answer:
-3-6y=9
Step-by-step explanation:
Timothy read 3,876 pages this school year. Amelia read 3,768 pages. Who read more pages this school year? E
Answers
Answer:
Timothy
Step-by-step explanation:
Timothy because he read 3,876 pages this year.
of the last 60 people who went to the cash register at the department store, 16 had blomd hair, 20 had black hair, and 3 had red hair. determine the empirical probability the next person will have brown hair
Answers
Answer: 20
Step-by-step explanation:
Answer: Plz don't come for me if its wrong but I think the answer is 21
Step-by-step explanation: Because there are 60 people in all and 16 had blond hair, 20 had black hair and 3 had red hair and 60-16-20-3=39 then you have to take 60-39 and you get 21
solutions to 2-variable equations y=-2x-5
Answers
Answer:(1, -3).
Step-by-step explanation:
If y=2x-5 is equation (1) and 4x-y=7 is equation (2), then substitute equation (1) in equation (2):
4x - (2x - 5) = 7
4x - 2x + 5 = 7
2x = 7-5
2x = 2
x = 1
Now substitute the value of x in equation (1) to find the value of y:
y = 2 (1) - 5
y = 2 - 5
y = -3
what is 0.5( -16p - 6) = ?
Answers
Answer:
−8p−3
Step-by-step explanation:
Four friends are training for long races. Eduardo ran 5.123 miles, Kandis ran 6.34 miles, Khaliyah ran 7.1 miles, and Moises ran 8 miles. b: Khaliyah ran how much further than Eduardo?
Answers
Answer:
1.977 miles
Step-by-step explanation:
Focus on how many miles Khaliyah and Eduardo are training.
Khaliyah = 7.100 miles
Eduardo = 5.123 miles
Difference = 7.100 - 5.123 = 1.977
We shuffle a deck of cards and deal three cards (without replacement). Find the probability that the first card is a queen, the second is a king, and the third is an ace.
Answers
Answer:
the probability that the first card is a queen, the second is a king, and the third is an ace is 0.000482655
Step-by-step explanation:
Given the data in the question;
we know that a deck of cards contains 52 cards
3 cards are dealt out without replacement
probability that first card is queen, the second is king and third is an ace will be;
P(First is a King, second is a Queen, third is an Ace) = [ 4/52 ] × [ 4/51 ] × [4/50]
= 64 / 132,600
= 0.000482655
Therefore, the probability that the first card is a queen, the second is a king, and the third is an ace is 0.000482655
Tara needs an $8,000 personal loan.
Which loan option would require her to pay back the least amount of money?
36-month loan with a 9% annual simple interest rate
42-month loan with a 7% annual simple interest rate
48-month loan with an 8% annual simple interest rate.
54-month loan with a 6% annual simple interest rate plaese awnser correctly ned today
Answers
Step-by-step explanation:
54-month loan with a 6% annual simple interest rate plaese awnser correctly ned today step by step can you tell me
Find the total fare with 15% tip: 1 passenger, 512 miles.
$9.89
$9.20
$10.23
$8.60
Answers
Answer:
37.92
Step-by-step explanation:
just add
Answer:
The answer would be $8.60
Step-by-step explanation:
np
In a class of 26 students, 11 are female and 10 have an A in the class. There are 2 students who are female and have an A in the class. What is the probability that a student is a female given that they have an A?
Answers
The probability that a student is a female given that they have an A is 0.2
How to determine the probability?The given parameters are:
Female = 11
A= 10
Female and A = 2
The probability is calculated using:
P(Female given A) = P(female and A)/P(A)
This gives
P(Female given A) = 2/10
Simplify
P(Female given A) = 0.2
Hence, the probability that a student is a female given that they have an A is 0.2
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Help needed for this math question.
Answers
What is the inverse function of f(x) = x
Answers
Inverse of the function f f(x)-1 = 1/f(x) (the Reciprocal
Write as a unit rate. 56 laps in 7 minutes = how many laps per minute?
(btw, I'm friending everyone who answers the question correctly and fast.)
Answers
Answer:
8 laps per minute
Step-by-step explanation:
56 laps in 7 minutes corresponds to the unit rate:
56 laps / 7 minutes = 8 laps/minute
That is : 8 laps per minute
Answer:
8 laps per min
Step-by-step explanation:
56 laps in 7 minutes!? They must be the flash
The area of Shawn's bedroom is 110 square feet. He places his bed, which is 7 feet long and 5 feet wide, in one corner of the bedroom. How much space will Shawn have left?
Answers
Answer:
gggg
Step-by-step explanation:
duxufif8fis5durris5is
What is the measure of angle M?
Answers
Answer:
35°
Step-by-step explanation:
4x+11 = 5x-24
5x-4x=x
x=24+11
x=35
What is the factored expression for 14 X +49
Answers
Answer:
7( 2x+7)
Step-by-step explanation:
14 X +49
Rewriting
2*7*x + 7*7
Factor out a 7 from each term
7( 2x+7)
Classify the pair of angles as adjacent, vertical, supplementary, complementary, or neither.
Answers
Answer:
adjacent supplementary angles
Step-by-step explanation:
The angles labeled 1 and 2 are adjacent angles which are called a linear pair. their measure add up to 180 deg, so they are adjacent and supplementary angles.
Thomas has constant speeds for both running and walking. When a down-escalator is moving, Thomas can run down it in 15 seconds or walk down it in 30 seconds. One day, when the escalator was broken (and stationary), it took Thomas 20 seconds to run down it. How long, in seconds, would it take Thomas to walk down the broken escalator?
ANSWER QUICK PLS ASAP
Answers
.....................
Answer:
40
Step-by-step explanation:
The ratio of the number of text messages sent by Diego to the number of text messages sent by his sister is 3 to 4. Diego sent 18 text messages. How many more text messages did his sister send?
Answers
Answer:
His sister sent 6 more messages than Diego.
Step-by-step explanation:
Ratio of Diego's messages to his sister's messages = 3 : 4
Text messages sent by Diego = 18
Text messages sent by his sister = x
Ratio = 18 : x
It is a proportional relationship,
3 : 4 :: 18 : x
Product of extremes = Product of means
3x = 18*4
3x = 72
[tex]\frac{3x}{3}=\frac{72}{3}\\x=24[/tex]
Difference = 24 - 18 = 6
Therefore,
His sister sent 6 more messages than Diego.
Please help I will mark brainlist
True or False: The magnitude of a resultant vector will always be larger than individual vectors that are both in the first quadrant
Answers
Answer:
I believe that it is false
What is the volume of the rectangular prism?
Answers
Answer:
72cm³
Step-by-step explanation:
The volume of the rectangular prism = Base area * Height
Base area = length * width
Base area = 6cm * 3cm = 18cm²
Height = 4cm²
volume of the rectangular prism = 18 * 4
volume of the rectangular prism = 72cm³
A circular swimming pool is 12 feet across and is enclosed by a fence. How long is the fence? (Round your answer to one decimal place.)
Answers
Answer:
the length of the fence is 37.7 feet
Step-by-step explanation:
The computation is given below:
Given that
Diameter = 12 feet
So, the radius is the half of the diameter = 6 feet
Now the length of the fence is
= 2 × π × r
= 2 × 3.14 × 6
= 37.68 feet
= 37.7 feet
Hence, the length of the fence is 37.7 feet
The length of the fence will be 37.7 feet.
Based on the information given, we are informed that the circular swimming pool is 12 feet across and is enclosed by a fence. We want to calculate the perimeter.
The perimeter of a circle will be:
= πd
where,
π = 3.142
d = 12 feet
Therefore, the length of the fence will be:
=πd
= 3.142 × 12
= 37.7 feet
The length of the fence is 37.7 feet.
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X+X+(60% of X)=180
Ez points plus brainliest
Answers
Answer:
x = 900/ 10 + 3fo
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
HELP MIDDLE SCHOOL QUESTION
Answers
Sweet Treats sells candy by the
pound as shown in the table:
Oscar says the unit rate is $3.99 per pound of candy
Olivia says the unit rate is 7.98 per pound of candy
A. Oscar
B. Olivia
Why did you use this answer
Answers
.) The total cost of a pizza and 3 drinks is $19. The price of the pizza is $10 and each drink is the
same price, d.
6) Which model represents the situation?
10
d
d
d
19
10
d
19
10-d
10-d
10-d
19
10
10
10
d
19
o
Answers
Answer:
The total cost of a pizza and 3 drinks is $19. The price of the pizza is $10 and each drink is the
same price, d.
6) Which model represents the situation?
Enter the missing number 57+[34+]=[57+34]+105
Answers
Answer:
105
Step-by-step explanation:
y = 5. – 7 2y = –12 -3x
Answers
Answer:
!! solved as -7(2y)= -12(-3x)
x= negative 1.943333
Step-by-step explanation: