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A relation `R = {(x, y) : x+2y=19, x,y \in A}` defined on the set `A = {1, 2, 3, ...., 10}`. Then find `R^{-1}`.

Ans: {(17, 1), (15, 2), (13, 3), (11, 4), (9, 5), (7, 6), (5, 7), (3, 8), (1, 9)}

A relation `R` defined by : `R ={(2x-5, x-3) : x \lt 12, x` even and `x \in \mathbb{N}}`, find the domain of definition and range of `R`.

Ans: {-1, 3, 7, 11, 15}, {-1, 1, 3, 5, 7}