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This question was created from MAT 230 Module 5 Homework


Let A = Z and R be the relation on A where a R b if and only if a + b is a multiple
of 4. Determine whether R is reflexive, irreflexive, symmetric, asymmetric,
antisymmetric, or transitive. For each property, either explain why R has that
property or give an example showing why it does not.

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Let A = Z
A relation R on A is defined as :
aRb <> a + b is a multiple of 4.
. 1+ 1 = 2 is not a multiple of 4.
.. (x, x) & R for at least one r E A => R is not reflexive.
. 2 + 2 = 4...

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