Question

Among the relations
S=\left\\{(a, b): a, b \in R -\\{0\\}, 2+\frac{a}{b}>\right\\}
and T=\left\\{(a, b): a, b \in R , a^2-b^2 \in Z\right\\},

• A. $S$ is transitive but $T$ is not
• B. both $S$ and $T$ are symmetric
• C. neither $S$ nor $T$ is transitive
• D. $T$ is symmetric but $S$ is not

Answer 1

Answer: (D)

$T$ is symmetric but $S$ is not

Answer 2

For relation T=a2−b2=−I
Then, (b, a) on relation R
⇒b2−a2=−I
∴T is symmetric
S={(a,b):a,b∈R−{0},2+ba​>0}
2+ba​>0⇒ba​>−2,⇒ab​<2−1​
If (b,a)∈S then
2+ab​ not necessarily positive
∴S is not symmetric
So, the correct option is (D) : $T$ is symmetric but $S$ is not