Question

Let $Y=\{1,2,3,4,5\},A=\{1,2\},B=\{3,4,5\}$ and $\varphi$ denotes null set. If $(A\times B)$ denotes cartesian product of the sets $A$ and $B$ , then $(Y\times A)\cap (7\times B)$ is

• A. Y
• B. A
• C. B
• D. $\varphi$

Answer 1

Answer: (D)

Given that, $Y=\{1,2,3,4,5\}$
$A=\{1,2\}$
$B=\{3,4,5\}$
$\therefore (Y\times A)=\{(1,1),(1,2),(2,1),(2,2),$
$(3,1),(3,2)(4,1),(4,2),(5,1),(5,2)\}$
and $(Y\times B)=\{(1,3),(1,4),(1,5),(2,3),$
$(2,4),(2,5),(3,3),(3,4),(3,5),(4,3),$
$(4,4),(4,5),(5,3),(5,4),(5,5)\}$
Now, $(Y\times A)\cap (Y\times B)=\varphi$ (null set)