Relations

To analyze the relation , we will check its properties:
1. Reflexivity: For to be reflexive, must be in for all . For , we need , which is not possible for any integer .
Hence, the relation is not reflexive.
2. Symmetry: For to be symmetric, if , then must also be in . If , then is not satisfied.
Hence, the relation is not symmetric.
3. Transitivity: For to be transitive, if and , then must also be in . If and , then we have , which does not equal , so the relation is not transitive.
Thus, the relation is neither reflexive, nor symmetric, nor transitive, and the correct answer is (B).