Question

Write the converse, inverse, and contrapositive of the conditional statement " If my cellphone will not charge, I will replace the battery "

Answer 1

See explanation

Explanation:

The given statement is " If my cellphone will not charge, I will replace the battery "

The hypothesis is

p: If my cell phone will not charge

The conclusion is

q: I will replace the battery

To write the converse, we switch the hypothesis and the conclusion:
`q\rightarrow p`

If I replace my battery, my cellphone will not charge.

To write the inverse, we negate the hypothesis and the conclusion:
`\\eg p\rightarrow \\eg q`

" If my cellphone will charge, I will not replace the battery "

The contrapositive is the negation of the the hypothesis and the and the conclusion after we switch them:
`\\eg q\rightarrow \\eg p`

If I will not replace my battery, my cellphone will charge.