Question

The inverse of a conditional statement is "If a number is negative, then it has a negative cube root.” What is the contrapositive of the original conditional statement?

Answer 1

Conditional: If p, then q
Converse: If q, then p
Inverse: If ~p, then ~q
Contrapositive: If ~q, then ~p
Conditional is the first step, turning the two parts into an if - then statement:

If x=7, then x2=49 -- True

CO nverse means C hange O rder

If x2=49, then x=7 -- Not always true (x could be −7 in this case and (−7)2=49, but x≠7)

Inverse is the negation of the original statement.

If x≠7, then x2≠49 -- Not always true (x could be −7 in this case and the result would still be 49 if you Square it)

CON trapositive means C hange O rder Negate

If x2≠49, then x≠7 -- Always true, given the conditional statement is true (this says that if x had been 7, then x2would have to equal 49 and if it is not 49, then it can't be 7 for sure)

Answer 2

''If a number has a negative cube root, then number is negative''.

Explanation:

We are given that

Inverse of conditional statement

''If a number is negative, then it has a negative cube root.''

We have to find the contrapositive of the original conditional statement.

Conditional statement: If p then q.

Inverse statement: If
`\\eg p`, then
`\\eg q`

Contrapositive :If
`\\eg q`, then
`\\eg p`

Therefore, contrapsotive statement of original conditional statement is give by

''If a number has a negative cube root, then number is negative''.