Question

Let $Y=\{1,2,3,4,5\},A=\{1,2\},B=\{3,4,5\}.$ If $A\times B$ denotes the cartesian product of sets $A$ and $B,$ then $(Y\times A)\cap (Y\times B)$ is

• A. $Y$
• B. $A$
• C. $B$
• D. Null set

Answer 1

The correct option is D Null set

We know that,
$(Y\times A)\cap (Y\times B)=\left(Y\right)\times (A\cap B)=Y\times \varphi =\varphi$