Answer
$a-\,\,p(A\times B)=\left \{ \varnothing ,\left \{ (1,u) \right \},\left \{ (1,v) \right \},\left \{ (1,u),(1,v) \right \} \right \}$
$b-\,\,\,$
$p(X\times Y)=\left \{ \varnothing ,\left \{ (a,x) \right \},\left \{ (a,y) \right \},\left \{ (b,x) \right \},\left \{ (b,y) \right \},\left \{ (a,x),(a,y) \right \},\left \{ (a,x),(b,x) \right \},\left \{ (a,x),(b,y) \right \},\left \{ (a,y),(b,x) \right \},\left \{ (a,y),(b,y) \right \},\left \{ (b,x),(b,y) \right \},\left \{(a,x),(b,x),(a,y) \right \},\left \{ (a,x),(b,x),(b,y) \right \},\left \{ (a,x),(a,y),(b,y) \right \},\left \{ (b,x),(a,y),(b,y) \right \},\left \{ (a,x),(b,x),(a,y),(b,y) \right \} \right \}$
Work Step by Step
$a.\,\,$
$A=\left \{ 1 \right \},B=\left \{ u,v \right \}$
$A\times B=\left \{ (1,u),(1,v) \right \} $
$p(A\times B)=\left \{ \varnothing ,\left \{ (1,u) \right \},\left \{ (1,v) \right \},\left \{ (1,u),(1,v) \right \} \right \}$
$b.\,\,\,$
$X=\left \{ a,b \right \},Y=\left \{ x,y \right \} $
$X\times Y=\left \{ (a,x),(a,y),(b,x),(b,y) \right \}$
$p(X\times Y)=\left \{ \varnothing ,\left \{ (a,x) \right \},\left \{ (a,y) \right \},\left \{ (b,x) \right \},\left \{ (b,y) \right \},\left \{ (a,x),(a,y) \right \},\left \{ (a,x),(b,x) \right \},\left \{ (a,x),(b,y) \right \},\left \{ (a,y),(b,x) \right \},\left \{ (a,y),(b,y) \right \},\left \{ (b,x),(b,y) \right \},\left \{(a,x),(b,x),(a,y) \right \},\left \{ (a,x),(b,x),(b,y) \right \},\left \{ (a,x),(a,y),(b,y) \right \},\left \{ (b,x),(a,y),(b,y) \right \},\left \{ (a,x),(b,x),(a,y),(b,y) \right \} \right \}$