enmobladatn
2022-07-27
Answered

Write a conditional statement. Write the converse, inverse and contrapositve for your statement and determine the truth value of each. If a statement’s truth value is false, give a counterexample.

You can still ask an expert for help

Wayne Everett

Answered 2022-07-28
Author has **19** answers

Conditional statement : If an animal is a cat, then it has four paws.

Converse: If an animal has 4 paws, then it is a cat.

There are other animals that have 4 paws that are not cats, so the converse is false

Inverse: If an animal is not a cat, then it does not have 4 paws.

There are animals that are not cats that have 4 paws, so the inverse is false.

Contrapositive: If an animal does not have 4 paws, then it is not a cat; True

Cats have 4 paws, so the contrapositive is true.

If a statement’s truth value is false, give a counterexample.

If an even number greater than 2 is prime, then 5 + 4 = 8.

An even number greater than 2 will never be prime, so the hypothesis is false. 5 + 4 is not equal to 8, so the conclusion is false. However, the conditional is true because the hypothesis is false.

{Note : If the hypothesis is false, the conditional statement is true, regardless of the truth value of the conclusion}

Converse: If an animal has 4 paws, then it is a cat.

There are other animals that have 4 paws that are not cats, so the converse is false

Inverse: If an animal is not a cat, then it does not have 4 paws.

There are animals that are not cats that have 4 paws, so the inverse is false.

Contrapositive: If an animal does not have 4 paws, then it is not a cat; True

Cats have 4 paws, so the contrapositive is true.

If a statement’s truth value is false, give a counterexample.

If an even number greater than 2 is prime, then 5 + 4 = 8.

An even number greater than 2 will never be prime, so the hypothesis is false. 5 + 4 is not equal to 8, so the conclusion is false. However, the conditional is true because the hypothesis is false.

{Note : If the hypothesis is false, the conditional statement is true, regardless of the truth value of the conclusion}

asked 2022-04-10

Find the derivative of $\mathrm{ln}(3+4\sqrt[3]{6+x})$.

asked 2021-10-21

Find the derivatives of the functions y = 8-t

asked 2021-09-22

Find the derivatives.

$y=(4{x}^{2}-6x)\mathrm{cos}(2-5x)$

asked 2021-03-10

Find the derivatives of the following functions.

$f\left(x\right)={\mathrm{cos}h}^{2}x$

asked 2020-11-29

For the following sets of variables, find all the relevant second derivatives. In all cases, first find general expressions for the second derivatives and then substitute variables at the last step.

asked 2021-10-23

The following questions are about the function $f(x,y)={x}^{2}{e}^{2xy}$ .

Find an equation of the tangent plane of f at the point (2,0, f(2,0))=(2,0,4).

Find an equation of the tangent plane of f at the point (2,0, f(2,0))=(2,0,4).

asked 2022-03-20

Evaluate the following limit **( IE do not use L'Hopital's rule).**

lim𝑥→4 sin(𝑥2−4𝑥) sin(𝑥2−10𝑥+24) .$$\underset{x\to 4}{lim}{\displaystyle \frac{\text{}\mathrm{sin}{\textstyle (}{x}^{2}-4x{\textstyle )}\text{}}{\text{}\mathrm{sin}{\textstyle (}{x}^{2}-10x+24{\textstyle )}\text{}}}.$$