If $P,Q$ and $R$ are subsets of a set $A$, then $R × (P^c \cup Q^c)^c =$
$(R × P) \cap (R × Q)$
$(R \times Q) \cup (R \times P)$
$(R \times P) \cup (R \times Q)$
None of these
If the set $A$ has $p$ elements, $B$ has $q$ elements, then the number of elements in $A × B$ is
If $(x+1, y-2)=(3,1),$ find the values of $\mathrm{x}$ and $\mathrm{y}$.
If two sets $A$ and $B$ have $99$ elements in common, then the number of elements common to the sets $A \times B$ and $B \times A$ is equal to
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 $(1, 3), (2, 5)$ and $(3, 3)$ are three elements of $A × B$ and the total number of elements in $A \times B$ is $6$, then the remaining elements of $A \times B$ are