Question

Let A = {1, 2, 3}. Which of the following is not an equivalence relation on A?

Options

• {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}

• None of these

• {(1, 1), (2, 2), (3, 3)}

• {(1, 1), (2, 2), (3, 3), (2, 3), (3, 2)}

Answer 1

None of these

Explanation:

If xRx for all x `in` R, a relation R on a non-empty set A is said to be reflexive. If xRy `=>` yRx, for any x, y `in` R, a relation R on a non-empty set A is said to be symmetric. If xRy and yRz `=>` xRz, for any x `in` R, a relation R on a non-empty set A is said to be transitive.

All three characteristics are satisfied by an equivalence relation.

None of the listed relations satisfy all three equivalence relation criteria.