2. Determine if each of the following relations is reflexive, anti-reflexive, symmetric, anti-symmetric, or transitive. Briefly...

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2. Determine if each of the following relations is reflexive, anti-reflexive, symmetric, anti-symmetric, or transitive. Briefly explain your answer for each property, even if the answer is “no.” (a) (5 points) Relation E is defined on Z such that for any integers x and y, xEy if xy is even. (b) (5 points) Relation O is defined on Z such that for any integers x and y, xOy if xy is odd. (c) (5 points) Relation A is defined on R such that for any real numbers x and y, xAy if |x − y| = 0. 2. Determine if each of the following relations is reflexive, anti-reflexive, symmetric, anti-symmetric, or transitive. Briefly explain your answer for each property, even if the answer is “no.” (a) (5 points) Relation E is defined on Z such that for any integers x and y, xEy if xy is even. (b) (5 points) Relation O is defined on Z such that for any integers x and y, xOy if xy is odd. (c) (5 points) Relation A is defined on R such that for any real numbers x and y, xAy if |x − y| = 0.

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Lets analyze each relation for reflexivity antireflexivity symmetry antisymmetry and transitivity a Relation E on the set of integers mathbbZ such that xEy if xy is even Reflexive A relation is reflex... View the full answer