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Determine reflexive, symmetric, antisymmetric, transitive, partial order and equivalence.

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Let R = {(1,1)(3,1)(2,2)(1,2)(3,3)(3,2)} on Z = {1,2,3}

Is R reflexive? Why?
Is R Symmetric? Why?
Is R antisymmetric? Why?
Is R transitive? Why?
Is R a partial order? Why?
Is R an equivalence relation?

https://brainmass.com/math/partial-differential-equations/reflexive-symmetric-antisymmetric-transitive-partial-order-4919

Solution Preview

1. R is reflexive since it contains (1,1),(2,2) and (3,3)
2. R is not symmetric. It contains (3,1) but not (1,3)
3. R is antisymmetric. We need to check that if (x,y) and (y,x) are in R then x=y. The only pairs (x,y) in R such ...

Solution Summary

It is determined if a relation is reflexive, symmetric, antisymmetric, transitive, partial order and its equivalence.

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