State whether each of the following statements are true or false. If the statement is false, rewrite the given statement 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 $P,Q$ and $R$ are subsets of a set $A$, then $R × (P^c \cup Q^c)^c =$
If $A, B$ and $C$ are any three sets, then $A \times (B \cup C)$ is equal to
Let $A=\{1,2,3\}, B=\{3,4\}$ and $C=\{4,5,6\} .$ Find
$(A \times B) \cap(A \times C)$
If $\left(\frac{x}{3}+1, y-\frac{2}{3}\right)=\left(\frac{5}{3}, \frac{1}{3}\right),$ find the values of $x$ and $y$