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How to prove "v" is not a commutative operation?
Give the operation "v" on the integers such that: avb = a|a-b|
*those are absolute value symbols*
And V does not stand in for any standard operation, it just IS. How do you prove the operation is not communtative?
An explanation with steps would also be greatly appreciated =)
1 Answer
- spoon737Lv 61 decade agoFavorite Answer
An operation * is commutative on a set A iff a*b = b*a for every a,b ∊ A. That means we only need to find a single counterexample to prove that v isn't commutative. But that's easy
-2v3 = -2|-2 - 3| = -2(5) = -10, and
3v-2 = 3|3 -(-2)| = 3(5) = 15
