Let $A = \{a, b, c\}$ and $B = \{1, 2\}$. Then the relation $R$ defined from set $A$ to set $B$ is a subset of which of the following?

State whether the following statement is true or false. If the statement is false,rewrite it correctly.
If $A = \{1, 2\}$ and $B = \{3, 4\}$,then $A \times \{B \cap \varnothing\} = \varnothing$.

If $A = \{1, 2, 3, 4\}$ and $B = \{a, b\}$,then the Cartesian product $A \times B$ is:

If $A = \{1, 2, 3, 4, \dots, 100\}$ and $B = \{51, 52, 53, \dots, 180\}$,then the number of elements in $(A \times B) \cap (B \times A)$ is:

Suppose that the number of elements in set $A$ is $p$,the number of elements in set $B$ is $q$ and the number of elements in $A \times B$ is $7$,then $p^2+q^2=$

If $A = \{1, 2, 4\}, B = \{2, 4, 5\}, C = \{2, 5\},$ then $(A - B) \times (B - C)$ is