(a) For A={-3,-2, …, 4} and B={1,2, …, 6}, determine S={(a, b) ∈A ×B: a^2+b^2=25} . (b) For C={

Question

(a) For A={-3,-2, …, 4} and B={1,2, …, 6}, determine S={(a, b) ∈A ×B: a^2+b^2=25} .  (b) For C={

Accepted Answer

Step 1: List out all possible pairs $(a,b)$ in $A u005Ctimes B$.u000A$Au003Du005C{u002D3,u002D2,u002D1,0,1,2,3,4u005C}$ and $Bu003Du005C

(a) For $A=\{-3,-2, \ldots, 4\}$ and $B=\{1,2, \ldots, 6\}$, determine $$ S=\left\{(a, b) \in A \times B: a^2+b^2=25\right\} \text {. } $$ (b) For $C=\{a \in B:(a, b) \in S\}$ and $D=\{b \in A:(a, b) \in S\}$, where $A, B, S$ are the sets in (a), determine $C \times D$.