If the statement, "If I am hungry, then I am not happy," is assumed to be true, is its inverse, "If I am not hungry, then I must be happy," also always true?

Question

lulubj · Answer

how is this math?

mathmate · Answer

@lulubj it's mathematical logic.

lulubj · Answer

Well then No because the correlation is not causation

lulubj · Answer

Also because statements that are true do not necessarily have true converses. We know that the person is always unhappy when they are hungry, but nothing in the sentence guarantees that if the person will always be happy when no longer hungry.

mathmate · Answer

@xjessiix33 
If a -> b is true, then its converse if b->a, which is not equivalent to a->b.
a->b  $\equiv$ ~b -> ~a   (its contrapositive).

mathmate · Answer

If statement P: "If I am hungry, then I am not happy," is assumed to be true, its converse, "If I am not hungry, then I must be happy," $not$ always true.
But contrapositive
"If I am happy, then I am not hungry" is always true if P is true.