Math Is Fun Forum

elthomas195

Member

Registered: 2011-12-19

Posts: 1

discrete math

a,b,c,∈Z^+ and a|bc, does it follow that a|b or a|c? Needing help I have never had this type of math before.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: discrete math

hi elthomas195

Welcome to the forum. 

Sorry.  It's so long ago that I did this,  I've forgotten which way you use the symbol |

EDIT: Found it on Wolfram Alpha.  Answer B is the one you want.

( .........So I'll do it both ways:

A.      I'm assuming that a|b means 'a' is divisible by 'b'

In that case, yes your statement is true.

if a|bc then

using associativity and commutativity

so a|b AND a|c

eg.  28|(2x7)  =>  28|2 and 28|7..............)

B.     But if I assume a|b means 'a' divides 'b'

then, no it is not true.

counterexample:

Hope that helps,

Bob

Last edited by Bob (2011-12-20 02:10:15)

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