(d): We have, $A = \{ 1,3,4,6,9\};B = \{ 2,4,5,8,10\}$\\ $R = \{\left( \left( a_{1},b_{1} \right),\left( a_{2},b_{2} \right) \right):a_{1} \leq b_{2}$ and $b_{1} \leq a_{2}\}$\\ At $a_{1} = 1$, there are 5 choices for $b_{2}$;\\ $a_{1} = 3$, there are 4 choices for $b_{2}$;\\ $a_{1} = 4$, there are 4 choices for $b_{2}$;\\ $a_{1} = 6$, there are 2 choices for $b_{2}$;\\ $a_{1} = 9$, there are 1 choice for $b_{2}$;\\ $\therefore$ Total ways for $\left( a_{1} \leq b_{2} \right) = 16$\\ Now, at $b_{1} = 2$, there are 4 choices for $a_{2}$;\\ $b_{1} = 4$, there are 3 choices for $a_{2}$;\\ $b_{1} = 5$, there are 2 choices for $a_{2}$;\\ $b_{1} = 8$, there are 1 choice for $a_{2}$\\ Total ways for $\left( b_{1} \leq a_{2} \right) = 10$\\ $\therefore$ Required number ways $= 16 \times 10 = 160$