## anonymous one year ago 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?

1. anonymous

how is this math?

2. mathmate

@lulubj it's mathematical logic.

3. anonymous

Well then No because the correlation is not causation

4. anonymous

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.

5. mathmate

@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).

6. mathmate

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.

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