If $A \times B = \{(a, x), (a, y), (b, x), (b, y)\}$,find $A$ and $B$.

If $A = \{0, 1\}$ and $B = \{1, 0\}$,then $A \times B$ is equal to

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 $B \times D$.

State whether the following statement is true or false. If the statement is false,rewrite the given statement correctly.
If $P = \{m, n\}$ and $Q = \{n, m\}$,then $P \times Q = \{(m, n), (n, m)\}$.

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

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