State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly.
If $A=\{1,2\}, B=\{3,4\},$ then $A \times\{B \cap \varnothing\}=\varnothing$
If the set $A$ has $3$ elements and the set $B=\{3,4,5\},$ then find the number of elements in $( A \times B ).$
If $P,Q$ and $R$ are subsets of a set $A$, then $R × (P^c \cup Q^c)^c =$
If $A$ and $B$ are two sets, then $A × B = B × A$ iff
If $(x+1, y-2)=(3,1),$ find the values of $\mathrm{x}$ and $\mathrm{y}$.