If A = {1, 2} and B = {3, 4}, and a relation R from A to B is defined as R = {(1, 3), (2, 4)}, then the inverse relation R⁻¹ is:

Model Answer & Options

Source: Extra Practice

{(3, 1), (2, 4)}

{(1, 3), (2, 4)}

{(3, 1), (4, 2)}

{(4, 1), (3, 2)}

Explanation

The inverse of a relation R, denoted by R⁻¹, is obtained by swapping the elements of each ordered pair in R. If (a, b) ∈ R, then (b, a) ∈ R⁻¹. For R = {(1, 3), (2, 4)}, the inverse is R⁻¹ = {(3, 1), (4, 2)}. Option A only swaps one pair. Option B is the original relation. Option D swaps the components incorrectly.

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