write down the convererse of

N is an odd integer = 2n is an even integer

and prove its false

Question

write down the convererse of

N is an odd integer => 2n is an even integer

and prove its false

mathmate · Answer

The converse of a statement is obtained by interchanging the roles of the antecedent and the consequent, as follows:
p : N is an odd integer
q : 2n is an even integer
The given statement is p->q and the converse is q->p.
The truth value of a statement and its converse bear no relationship whatsoever.

In the given case,
p->q is true.
Its converse
q->p => if 2n is an even integer, then n is a odd integer 
may or may not be true.
Take the case of 2n=6, then n=3 IS an odd integer.
In the case of 2n=8, then n=4 is NOT an odd integer.