3. (6 points) Disprove the following: For all a, b, c E Z, if aſbc, then...

Question

Question

3. (6 points) Disprove the following: For all a, b, c E Z, if aſbc, then aſb or b|c.

Answer 1

Answer #1

To disprove, only one counter example is sufficient.

False let 6 divides 6 a=6 6/23 neither neither bs 2 c=3 = 6/6 = 6/2 no 6 divides But .. 643. I.e a not to divides 3 Here it a

Answer 2

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