Let the relation R be defined on the set A = {1, 2, 3, 4, 5} by R = {(a, b) : |a^2 – b^2| < 8}. Then R is given by _______.

Question

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Let the relation R be defined on the set
A = {1, 2, 3, 4, 5} by R = {(a, b) : |a² – b²| < 8}. Then R is given by _______.

Answer 1

Given that, A = {1, 2, 3, 4, 5} and R = {(a, b) : |a² – b²| < 8}

Let us check the relation for a=1,b=2

⇒ |12 – 22| = |-3|= 3 < 8

⇒ (1,2) ∈ R

Similarly, we can check for all the ordered pairs of (a,b) which satisfies the relation.

Hence, R = {(1,1),(1,2),(2,1),(2,2),(2,3),(3,2),(3,3),(3,4),(4,3), (4,4),(5,5)}