Relations and Functions (Class 12) · Question 34

The relation R = \(x, y) : x, y Z and x + y is even\ is:

1. reflexive and transitive but not symmetric
2. reflexive and symmetric but not transitive
3. an equivalence relation
4. symmetric and transitive but not reflexive

Answer

(3) an equivalence relation

Solution

Reflexive: x + x = 2x is even for every x Z (x, x) R.

Symmetric: x + y even y + x even (y, x) R.

Transitive: x + y and y + z even

x + z = (x + y) + (y + z) - 2y is even (x, z) R.

R is an equivalence relation.

Answer: (3)