Question

Conditional: If x is odd, then 3x is odd

Converse: If 3x is odd, then x is odd
Inverse:If x is not odd, then 3x is not odd
Contrapositive:If 3x is not odd, then x is not odd
Which of the above are true statements?
A) If x is odd, then 3x is odd.
B) If 3x is odd, then x is odd.
C) If x is not odd, then 3x is not odd.
D) If 3x is not odd, then x is not odd.

Answer 1

The correct statements are A, C, and D.

Step-by-step explanation:

In this question, we are given four statements:

A) If x is odd, then 3x is odd.

B) If 3x is odd, then x is odd.

C) If x is not odd, then 3x is not odd.

D) If 3x is not odd, then x is not odd.

To determine which statements are true, we need to analyze them:

A) If x is odd, then 3x is odd.

This statement is true. If x is odd, when we multiply it by 3, the result will still be odd.

B) If 3x is odd, then x is odd.

This statement is false. Just because 3x is odd, it doesn't mean that x has to be odd. For example, if x is 2, then 3x is 6, which is even.

C) If x is not odd, then 3x is not odd.

This statement is true. If x is not odd, it means x is even. And if x is even, when we multiply it by 3, the result will still be even.

D) If 3x is not odd, then x is not odd.

This statement is true. If 3x is not odd, it means 3x is even. And if 3x is even, it means x is even.

So, the correct statements are A, C, and D.