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?
If $aN = \{ ax:x \in N\} $ and $bN \cap cN = dN$, where $b$, $c \in N$ are relatively prime, then
If $A$ and $B$ are two sets then $(A -B) \cup (B -A) \cup (A \cap B)$ is equal to
Find the union of each of the following pairs of sets :
$X =\{1,3,5\} \quad Y =\{1,2,3\}$
Show that the following four conditions are equivalent:
$(i)A \subset B\,\,\,({\rm{ ii }})A - B = \phi \quad (iii)A \cup B = B\quad (iv)A \cap B = A$