let A = {1,2,3} and B = {2,3,4}. Determine the following:(a) (A X B) ∩ (B X A) (b) (A ∩ B) X (B ∩ A)

Answer:a) [tex](A\times B)\cap (B\times A)=\{(2,2),(3,3),(2,3),(3,2)\}[/tex]b) [tex](A\cap B)\times (B\cap A)=\{(2,2),(2,3),(3,2),(3,3)\}[/tex]Step-by-step explanation:Given : Let A = {1,2,3} and B = {2,3,4}.To find : Determine the following a) [tex](A\times B)\cap (B\times A)[/tex]b) [tex](A\cap B)\times (B\cap A)[/tex]Solution : a) [tex](A\times B)\cap (B\times A)[/tex][tex]A\times B=\{a,b\}|a\in A,b\in B[/tex][tex]A\times B=\{(1,2),(1,3),(1,4),(2,2),(2,3),(2,4),(3,2),(3,3),(3,4)\}[/tex][tex]B\times A=\{(2,1),(2,2),(2,3),(3,1),(3,2),(3,3),(4,1),(4,2),(4,3)\}[/tex][tex](A\times B)\cap (B\times A)=\{(2,2),(3,3),(2,3),(3,2)\}[/tex]b) [tex](A\cap B)\times (B\cap A)[/tex][tex]A\cap B=\{2,3\}[/tex][tex]B\cap A=\{2,3\}[/tex][tex](A\cap B)\times (B\cap A)=\{(2,2),(2,3),(3,2),(3,3)\}[/tex]