(d) : Given, $A = \{ 1,2,3,4,5,6,7\}$ and $R = \{(x,y) \in A \times A:x + y = 7\}$ For Reflexive : Let $y = x$ So, $x + x = 7 \Rightarrow x = \frac{7}{2}$, which is not possible. So, given relation is not reflexive. For symmetric : $xRy \Rightarrow x + y = 7$ $\Rightarrow y + x = 7\therefore xRy \Rightarrow yRx$ Hence, given relation is symmetric. For transitive : Let $xRy$ and $yRz \Rightarrow x + y = 7$ and $y + z = 7$ But it does not implies that, $x + z = 7$ So, $R$ is not transitive.