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2.Relations and Functions
easy
If $A \times B=\{(a, x),(a, y),(b, x),(b, y)\} .$ Find $A$ and $B$
A
$\{ a,b\} $ and $\{ x,y\} $
B
$\{ a,b\} $ and $\{ x,y\} $
C
$\{ a,b\} $ and $\{ x,y\} $
D
$\{ a,b\} $ and $\{ x,y\} $
Solution
If is given that $A \times B=\{(a, x),(a, y),(b, x),(b, y)\}$
We know that the Cartesian product of two non-empty sets $P$ and $Q$ is defined as
$P \times Q=\{(p, q): p \in P, q \in Q\}$
$\therefore $ $A$ is the set of all first elements and $B$ is the set of all second elements.
Thus, $A=\{a, b\}$ and $B=\{x, y\}$
Standard 11
Mathematics
