If the sets $A$ and $B$ are defined as $A = \{ (x,\,y):y = {1 \over x},\,0 \ne x \in R\} $ $B = \{ (x,y):y = - x,x \in R\} $, then
$A \cap B = A$
$A \cap B = B$
$A \cap B = \phi $
None of these
Let $A$ and $B$ be subsets of a set $X$. Then
If $S$ and $T$ are two sets such that $S$ has $21$ elements, $T$ has $32$ elements, and $S$ $\cap \,T$ has $11$ elements, how many elements does $S\, \cup$ $T$ have?
Find the union of each of the following pairs of sets :
$A=\{a, e, i, o, u\} B=\{a, b, c\}$
For any sets $\mathrm{A}$ and $\mathrm{B}$, show that
$P(A \cap B)=P(A) \cap P(B).$
If $A, B, C$ are three sets, then $A \cap (B \cup C)$ is equal to