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Discrete math - proof of divisibility question

  1. Aug 25, 2012 #1
    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.


    then c=bz
    and c = bg doesn't hold.
  2. jcsd
  3. Aug 25, 2012 #2


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    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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