Chapter 7.1, Problem 25ES

Let $A=\left\{2,3,5\right\}$ and $B=\left\{x,y\right\}.$ Let $p_1$ and $p_2$ be the projections of $A\times B$ onto the first and second coordinates. That is, for each pair $\left(a,b\right)\in A\times B,p_1\left(a,b\right)=a$ and $p_2\left(a,b\right)=b.$

a. Find $p_1\left(2,y\right)$ and $p_1\left(5,x\right).$ What is the range of $p_1?$

b. Find $p_2\left(2,y\right)$ and $p_2\left(5,x\right).$ What is the range of $p_2?$