$A = \{1,2,3,4......100\}, B = \{51,52,53,...,180\}$, then number of elements in $(A \times B) \cap (B \times A)$ is
$1800$
$1600$
$2500$
$1500$
If $A = \{ 1,\,2,\,3,\,4\} $; $B = \{ a,\,b\} $ and $f$ is a mapping such that $f:A \to B$, then $A \times B$ is
Let $A$ and $B$ be two sets such that $n(A)=3$ and $n(B)=2 .$ If $(x, 1),(y, 2),(z, 1)$ are in $A \times B$, find $A$ and $B$, where $x, y$ and $z$ are distinct elements.
If $(x+1, y-2)=(3,1),$ find the values of $\mathrm{x}$ and $\mathrm{y}$.
If $P=\{a, b, c\}$ and $Q=\{r\},$ form the sets $P \times Q$ and $P \times Q$ Are these two products equal?
If two sets $A$ and $B$ have $99$ elements in common, then the number of elements common to the sets $A \times B$ and $B \times A$ is equal to