Among the relations S = a , b : a , b ∈ R - 0 , 2 + a b > 0 and T = a , b : a , b ∈ R , a 2 - b 2 ∈ Z ,

Step-by-step solution

Given, a ,   b   ∈   I and relation T is defined as a 2 - b 2 ∈ I Now if a 2 - b 2 ∈ I so b 2 - a 2 will also be integer, for example if 5 2 - 4 2 = 9 is integer then 4 2 - 5 2 = - 9 is also a integer, Now checking transitive, If 4 2 - 3 2 = 7 is an integer, 3 2 - 2 2 = 5 is an integer then 4 2 - 2 2 = 12 is also an integer, hence we can say that T is symmetric and transitive, Now checking relation S which is defined as 2 + a b > 0 , So, if we replace a b by - 1 9 then 2 + a b &