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
$\{(a, 1), (3, b)\}$
$\{(a, 2), (4, b)\}$
$\{(1, a), (1, b), (2, a), (2, b), (3, a), (3, b), (4, a), (4, b)\}$
None of these
State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly.
If $A=\{1,2\}, B=\{3,4\},$ then $A \times\{B \cap \varnothing\}=\varnothing$
$A = \{1,2,3,4......100\}, B = \{51,52,53,...,180\}$, then number of elements in $(A \times B) \cap (B \times A)$ is
If $A, B$ and $C$ are any three sets, then $A \times (B \cup C)$ is equal to
Let $A = \{1, 2, 3, 4, 5\}; B = \{2, 3, 6, 7\}$. Then the number of elements in $(A × B) \cap (B × A)$ is
If two sets $A$ and $B$ are having $99$ elements in common, then the number of elements common to each of the sets $A \times B$ and $B \times A$ are