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 $A \times\{B \cap \varnothing\}=\varnothing$
If $n(A) = 4$, $n(B) = 3$, $n(A \times B \times C) = 24$, then $n(C) = $
If $P=\{a, b, c\}$ and $Q=\{r\},$ form the sets $P \times Q$ and $P \times Q$ Are these two products equal?
If $A, B$ and $C$ are any three sets, then $A \times (B \cup C)$ is equal to
If $A = \{1, 2, 4\}, B = \{2, 4, 5\}, C = \{2, 5\},$ then $(A -B) × (B -C)$ is