Discrete math - proof of divisibility question

Thread starter dgamma3
Start date Aug 25, 2012
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Discrete Discrete math Divisibility Proof

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The statement "If a|b and a|c, then one (or both) of b|c or c|b holds" is false. A counter-example is provided with a=5, b=10, and c=15, demonstrating that neither 10 divides 15 nor 15 divides 10. The discussion highlights that constructing a counter-example effectively disproves the claim. The complexity of the proof is questioned, suggesting that simpler examples could suffice. Ultimately, the counter-example clearly illustrates the falsity of the original statement.

Aug 25, 2012

dgamma3

is this true or false:

If a|b and a|c, then one (or both) of b|c or c|b holds.

if I want to disprove this, can I:

let a = 5, x = 2 and y = 3.

b=ax
c=ay

then c=bz
and c = bg doesn't hold.

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Aug 25, 2012

Bacle2

Science Advisor

Why make it so complicated? You constructed a counter-example:

a=5 , b=10 c=15 , and neither 10|15 nor 15|10.

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