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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 = {\(\Big(x,\frac{1}{x}\Big):x \,is\,an\,interger,0<x<5\)}

(iii) R ={(x, y) : x + 2y = 8 and x, y ϵ N} 

(iv) R = {(x, y), : y = |x – 1|, x ϵ Z and |x| ≤ 3}

1 Answer

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

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

Range(R) = {y: (x, y)ϵR} = {1, 4, 9} 

(ii) Given: 

(iii) 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)ϵR} = {2, 4, 6} 

Range(R) = {y: (x, y)ϵR} = {1, 2, 3} 

(iv) Given: R = {(x, y): y = |x – 1|, x ϵ Z and |x| ≤ 3} 

Dom(R) = {x: (x, y)ϵR} = {-3, -2, -1, 0, 1, 2, 3} 

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

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