Let A = {1, 2, 3, ......., 45} and R be the relation 'is square of' in A. Which of the following is false?

At least one is false.

We have (1)² = 1, (2)² = 4, (3)² = 9, (4)² = 16, (5)² = 25, (6)² = 36

∴ R = {(1, 1), (4, 2), (9, 3), (16, 4), (25, 5), (36, 6)}

Domain of R = {x ; (x, y) ∈ R} = {1, 4, 9, 16, 25, 36}

Range of R = {y ; (x, y) ∈ R} = {1, 2, 3, 4, 5, 6}

Hence (4) is the correct answer.