This is part of a question (PS: the question just asked me to write converse, inverse, contrapositive counterparts. My question is not related to the question itself):
Statement: ∀n ∈ Z, if (6 | n), then (2 | n) and (3 | n).
Converse: ∀n
∈ Z, if (2 | n) and (3 | n), then (6 | n).
I understand that converse statements are NOT logically equivalent to conditional statements.
For them to be logically inequivalent, we just need one instance where predicates have opposite truth values for a particular chosen value of the predicate variable.
But I'm unable to find that one instance (counter-example) that would prove that the converse and the original are not logically equivalent.
Best Answer
For your statement, the converse is true since $\mathrm{lcm}(2,3)=6$ but it isn't always.
$\forall\ n \in \mathbb{Z},$ if $12 \mid n,$ then $2 \mid n$ and $3 \mid n$ but the converse is not true.