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
$\{(a, 1), (3, b)\}$

- B
$\{(a, 2), (4, b)\}$

- C
$\{(1, a), (1, b), (2, a), (2, b), (3, a), (3, b), (4, a), (4, b)\}$

- D
None of these

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.

The Cartesian product $A$ $\times$ $A$ has $9$ elements among which are found $(-1,0)$ and $(0,1).$ Find the set $A$ and the remaining elements of $A \times A$.

If $A = \{2, 3, 5\}, B = \{2, 5, 6\},$ then $(A -B) × (A \cap B)$ is

Let $A=\{1,2\}, B=\{1,2,3,4\}, C=\{5,6\}$ and $D=\{5,6,7,8\} .$ Verify that

$A \times C$ is a subset of $B \times D$

If $A, B$ and $C$ are any three sets, then $A \times (B \cup C)$ is equal to