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."
