Given A = {–2, –1, 0, 1, 2}, which of the following relations on A have both domain and range equal to A? -Maths 9th

Given A = {–2, –1, 0, 1, 2}, which of the following relations on A have both domain and range equal to A? -Maths 9th
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1 Answer

Answer :

(d) (i) and (iii)Let us examine the domain and range of the each relation individually: (i) R : “is equal to” means R = {(a, b) : a = b, a ∈ A, b ∈A} ∴ R = {(–2, –2), (–1, –1), (0, 0), (1, 1), (2, 2)} ∴ Domain of R = {–2, –1, 0, 1, 2} and Range of R = {–2, –1, 0, 1, 2} Hence both are equal and equal to A. (ii) R : “is the multiplicative inverse of ” means R = {(a, b): ab = 1, a ∈ A, b ∈ A} ∴ R = {(–1, –1), (1, 1)} Here domain = {–1, –1}, range = {–1, 1}. (iii) R : “is the additive inverse of ”means R = {(a, b) : a = –b, a ∈ A, b ∈ A} ∴ R = {(–2, 2), (–1, 1), (0, 0), (1, –1), (2, –2)} Hence domain = {–2, –1, 0, 1, 2} and range = {2, 1, 0, –1, –2} Both are equal and equal to A. (iv) R : “is less than ” means R = {(a, b) : a < b, a ∈ A, b ∈ A} ∴ R = {(–2, –1), (–2, 0), (–2, 1), (–2, 2), (–1, 0), (–1, 1), (–1, 2), (0, 1), (0, 2), (1, 2)} Here domain = {–2, –1, 0, 1} and range = {–1, 0, 1, 2}. ∴ Relations given in (i) and (iii) satisfy the given condition.
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