# Binary Operations and Equivalence

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• Oct 20th 2012, 09:47 PM
ducked
Binary Operations and Equivalence
Hi I have this question and have no idea how to go about it.
Attachment 25303

Any help would be greatly appreciated.
• Oct 21st 2012, 01:10 AM
chiro
Re: Binary Operations and Equivalence
Hey ducked.

Can you show us what you have tried? You have three properties to prove: X ~ X, X ~ Y <=> Y ~ X, and X ~ Y and Y ~ Z <=> X ~ Z. Some hints include that if a^2 = b^2 (MOD 5) then b^2 = a^2 (MOD 5) (congruence arithmetic).
• Oct 21st 2012, 02:08 AM
ducked
Re: Binary Operations and Equivalence
thanks chiro

pretty average at this subject but i think for part a:
so if a^2 ≡ b^2 (mod 5) then b^2 ≡ a^2 (mod 5) then is it symmetric ? Also should be transitive as if a^2 ≡ b^2 (mod 5) and b^2 ≡ c^2 (mod 5) then a^2 ≡ c^2 (mod 5).

part b: can we write the set A x A so {(1,1),(1,2),(2,1),(2,2)} and then find all binary relations that are reflexive. thus not having to write out all 16 possible binary relations?

think im rambling dont really know how to put it together