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.

Respuesta :

Contrapositive statement definition: 
Conditional: [tex]A\Rightarrow B[/tex]
Contrapositive: [tex]\neg B \Rightarrow \neg A[/tex]

Conditional: [tex]6x \neq 24 \Rightarrow x \neq 4[/tex]
Contrapositive: 
[tex]\neg(6x \neq 24) \Rightarrow \neg(x \neq 4) \\6x=24 \Rightarrow x=4[/tex]

Therefore, correct answer is A.
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