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?

Let $A, B, C$ be three sets such that $n(A \cap B) = n(B \cap C) = n(C \cap A) = n(A \cap B \cap C) = 2$. Then $n((A \times B) \cap (B \times C))$ is equal to -

State whether the following statement is true or false. If the statement is false,rewrite it correctly.
If $A$ and $B$ are non-empty sets,then $A \times B$ is a non-empty set of ordered pairs $(x, y)$ such that $x \in A$ and $y \in B$.

If $R$ is the set of all real numbers,what do the Cartesian products $R \times R$ and $R \times R \times R$ represent?

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 $A, B,$ and $C$ are three sets,then $A \times (B \cap C)$ is equal to: