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Basic Proof by Contradiction of the Zero Product Property

Prove the Zero Producty Property in real numbers that:
If ab=0 then a=0 or b=0

(Question is repeated in attachment)


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I'm going to call our assumption (ab=0) P, and the thing we want to prove (a=0 or b=0) Q. So we want to show that P => Q (P implies Q) and we can do this by contradiction: assume P and ~Q (the negation of Q) and show that there is a contradiction with this assumption.

I know what P is (ab=0) but what is ~Q? It is ~(a=0 or b=0). Now ...

Solution Summary

This solution shows a proof that if ab=0, then a=0 or b=0. Gives an introduction to proving things by contradiction.