Question

Let $ Y = \{1,2,3,4,5\}, A = \{1, 2\}, B = \{3,4,5\}$ and $\phi$ 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. $ \phi $

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)=\phi $ (null set)