Find the domain and range of each of the relations given below: (i) R = {(–1, 1), (1, 1), (–2, 4), (2, 4), (2, 4), (3, 9)}
(ii)R ={(x, y) : x + 2y = 8 and x, y ϵ N}
(iii) R = {(x, y), : y = |x – 1|, x ϵ Z and |x| ≤ 3}
Find the domain and range of each of the relations given below: (i) R = {(–1, 1), (1, 1), (–2, 4), (2, 4), (2, 4), (3, 9)}
(ii)R ={(x, y) : x + 2y = 8 and x, y ϵ N}
(iii) R = {(x, y), : y = |x – 1|, x ϵ Z and |x| ≤ 3}

Answer : (i) Given: R = {(–1, 1), (1, 1), (–2, 4), (2, 4), (2, 4), (3, 9)}

Dom(R) = {x: (x, y)    R} = {-2, -1, 1, 2, 3}

Range(R) = {y: (x, y)    R} = {1, 4, 9}

 

(ii) Given: R = {(x, y): x + 2y = 8 and x, y ϵ N} That means, R = {(2, 3), (4, 2), (6, 1)}

Dom(R) = {x: (x, y)    R} = {2, 4, 6}

Range(R) = {y: (x, y)    R} = {1, 2, 3}

(iii)Given: R = {(x, y): y = |x – 1|, x ϵ Z and |x| ≤ 3} Dom(R) = {x: (x, y) R} = {-3, -2, -1, 0, 1, 2, 3}

Range(R) = {y: (x, y)    R} = {0, 1, 2, 3, 4}