Question

Let set X = {1, 2, 3} and a relation R is defined in X as: R = {(1, 3), (2, 2), (3, 2)}, then minimum ordered pairs which should be added in relation R to make it reflexive and symmetric are ______.

Options

• {(1, 1), (2, 3), (1, 2)}

• {(3, 3), (3, 1), (1, 2)}

• {(1, 1), (3, 3), (3, 1), (2, 3)}

• {(1, 1), (3, 3), (3, 1), (1, 2)}

Answer 1

Let set X = {1, 2, 3} and a relation R is defined in X as: R = {(1, 3), (2, 2), (3, 2)}, then minimum ordered pairs which should be added in relation R to make it reflexive and symmetric are `underlinebb({(1, 1), (3, 3), (3, 1), (2, 3)})`

Explanation:

i. R is reflexive if it contains {(1, 1), (2, 2) and (3, 3)}.

Since, (2, 2) ∈ R. So, we need to add (1, 1) and (3, 3) to make R reflexive.

ii. R is symmetric if it contains {(2, 2), (1, 3), (3, 1), (3, 2), (2, 3).

Since, {(2, 2), (1, 3), (3, 2)} ∈ R. So, we need to add (3, 1) and (2, 3).

Thus, minimum ordered pairs which should be added in relation R to make it reflexive and symmetric are {(1, 1), (3, 3), (3, 1), (2, 3)}.