Question

Write down the converse and contrapositive. If 2 divides x, then x is an even number. Hint call this (p?q)

Answer 1

Answer:  

The converse and contrapositive of the given conditional statement are :

Converse : "If x is an even number, then 2 divides x".

Contrapositive : "If x is not an even number, then 2 does not divide x."

Step-by-step explanation:  We are given to write the converse and contrapositive of the following conditional statement :

"If 2 divides x, then x is an even number."

Let us consider that

p : 2 divides x

and

q : x is an even number.

We know that

the CONVERSE of a conditional statement p ⇒ q is written as q ⇒ p.

So, the converse of the given statement is

"If x is an even number, then 2 divides x".

The CONTRAPOSITIVE of the conditional statement  p ⇒ q is written as ~q ⇒ ~p (where ~p stands for the negation of p).

So, the contrapositive of the given statement is

"If x is not an even number, then 2 does not divide x."

Thus, the converse and contrapositive of the given statement are :

Converse : "If x is an even number, then 2 divides x".

Contrapositive : "If x is not an even number, then 2 does not divide x."