Complete the proof of the following statement by filling in the blanks, and
answer the questions.
Let x, y in Z. If 3|x or 3|y then 3|xy.
Proof Technique:
Hypothesis, P:
Conclusion, Q:
PROOF:
Assume that 3|x or 3|y.
Without loss of generality, assume that 3|x. Then x = _____ for some z in Z.
Now consider,
xy = _____ = _____ = _____ , where _____ = _____- in Z.
Therefore, 3 divides ____ or 3 | ____.
Hence, 3 divides xy if 3 divides ______ or 3 divides ______.
Q.E.D.
1. What should be mentioned in a complete proof?
2. What could be a more effective proofing technique and why?
