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Amongst the properties {reflexivity, symmetry, antisymmetry, transitivity} the relation R={(a,b) ∈ N^2 | a!= b} satisfies _______ property.(a) symmetry(b) transitivity(c) antisymmetry(d) reflexivityThe question was asked by my college professor while I was bunking the class.The query is from Closure on Relations topic in division Relations of Discrete Mathematics

Answer» RIGHT choice is (a) symmetry

To elaborate: It is not reflexive as aRa is not POSSIBLE. It is symmetric as if aRb then BRA. It is not antisymmetric as aRb and bRa are possible and we can have a!=b. It is not transitive as if aRb and bRc then ARC need not be true. This is VIOLATED when c=a. So the answer is symmetry property.


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