Question

Write the contrapositive of the conditional statement and then determine if the conditional statement and the contrapositive are true or false.

If 6x _ 24, then x _ 4.

A. If 6x = 24, then x = 4. The conditional statement and the contrapositive are both true.

B. If x = 4, then 6x = 24. The conditional statement and the contrapositive are both true.

C. If x = 4, then 6x = 24. The conditional statement is false, and the contrapositive is true.

D. If x _ 4, then 6x _ 24. The conditional statement and the contrapositive are both false.

Answer 1

Contrapositive statement definition:
Conditional:
`A\Rightarrow B`
Contrapositive:
`\\eg B \Rightarrow \\eg A`

Conditional:
`6x \\eq 24 \Rightarrow x \\eq 4`
Contrapositive:

`\\eg(6x \\eq 24) \Rightarrow \\eg(x \\eq 4) \\6x=24 \Rightarrow x=4`

Therefore, correct answer is A.