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(d) : For relation T = a2 − b2 ∈ IT = a^{2} - b^{2} \in I\\T = a2 − b2 ∈ I Then, (b,a)(b,a)(b,a) on relation R ⇒ b2 − a2 in IR \Rightarrow b^{2} - a^{2} in I\\R ⇒ b2 − a2 in I ∴ T\therefore T∴ T is symmetric, S = { (a,b):a,b ∈ R − { 0},2 + ab > 0 }\\S = \left\{ (a,b):a,b \in R - \{ 0\},2 + \frac{a}{b} > 0 \right\}\\S = { (a,b):a,b ∈ R − { 0},2 + ba > 0 } 2 + ab > 0 ⇒ ab > − 2 ⇒ ba > − 122 + \frac{a}{b} > 0 \Rightarrow \frac{a}{b} > - 2 \Rightarrow \frac{b}{a} > \frac{- 1}{2}\\2 + ba > 0 ⇒ ba > − 2 ⇒ ab > 2− 1 If (b,a) in S(b,a) in S(b,a) in S then 2 + ba2 + \frac{b}{a}2 + ab not necessarily positive ∴ S\\ \therefore S ∴ S is not symmetric.
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