In 9-33, determine whether the given relation is reflexive symmetric, transitive, or none of these. Justify your answer.
O is the relation defined on Z as follows: For every is odd.
To justify whether the given relation is reflexive, symmetric, transitive, or none of these.
O is the relation defined on Z as follows:
For all is odd.
Let us consider the given relation as
The relation O is reflexive if for every element
O is reflexive if it contains for all
We note that O does not contain because and 0 is not odd, thus O is not reflexive.
Thus, not reflexive
The relation O on a set A is symmetric if .
Let us assume that By definition of O
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