Question

If R s a relation defined on set A ={1, 2, 3} by the rule (a,b) $\in R\iff \left|a^2-b^2\right|\le 5,$ then R^-1 =____________________.

Answer 1

Given: R = {(a, b): $\left|a^2-b^2\right|\le 5$}, where A = {1, 2, 3} and a, b ∈ A.

R = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 2), (3, 3)}

Therefore, R⁻¹ = {(1, 1), (2, 1), (1, 2), (2, 2), (3, 2), (2, 3), (3, 3)} = R

Hence, if R is a relation defined on set A = {1, 2, 3} by the rule (a,b) $\in R\iff \left|a^2-b^2\right|\le 5,$ then R^-1 = R.