Question 20

The relation $$R=\left\{(x,y):x,y \in \mathbb{Z}\text{ and }x+y\text{ is even}\right\}$$ is:

Solution

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R = {(x,y): x+y is even}. Reflexive: x+x=2x (even) ✓. Symmetric: if x+y even, y+x even ✓. Transitive: if x+y and y+z are even, then x+z = (x+y)+(y+z)-2y (even) ✓.

The correct answer is Option 2: equivalence relation.

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