Let $Y = \left\{ 1,\ 2,\ 3,\ 4,\ 5 ight\},\ A\left\{ 1,\ 2 ight\},\ B = \{ 3,\ 4,\ 5\}$ and $\phi$ denotes null set. If $(A imes B)$ denotes cartesian product of the sets $A$ and $B$; then $(Y imes A) \cap (Y imes B)$ is

Question

Let $Y = \left\{ 1,\ 2,\ 3,\ 4,\ 5 ight\},\ A\left\{ 1,\ 2 ight\},\ B = \{ 3,\ 4,\ 5\}$ and $\phi$ denotes null set. If $(A 	imes B)$ denotes cartesian product of the sets $A$ and $B$; then $(Y 	imes A) \cap (Y 	imes B)$ is

Dr. Abubacker · Accepted Answer

(d)
$(Y 	imes A) = \{(1,\ 1),\ (1,\ 2),\ (2,\ 1),\ (2,\ 2),\$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (3,\ 1),\ (3,\ 2),\ (4,\ 1),\ (4,\ 2),\ (5,\ 1),\ (5,\ 2)\}$
And$(Y 	imes B) = \{(1,\ 3),\ (1,\ 4),\ (1,\ 5),\ (2,\ 3),\$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2,\ 4),\ (2,\ 5),\ (3,\ 3),\ (3,\ 4),\ (3,\ 5),\ (4,\ 3),\$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (4,\ 4),\ (4,\ 5),\ (5,\ 3),\ (5,\ 4),\ (5,\ 5)\}$
$	herefore(Y 	imes A) \cap (Y 	imes B) = \phi$

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

Explanation

Reviewed by Dr. Abubacker

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