Let $\mathrm{X}=\{\mathrm{n} \in \mathrm{N}: 1 \leq \mathrm{n} \leq 50\} .$ If $A=\{n \in X: n \text { is a multiple of } 2\}$ and $\mathrm{B}=\{\mathrm{n} \in \mathrm{X}: \mathrm{n} \text { is a multiple of } 7\},$ then the number of elements in the smallest subset of $X$ containing both $\mathrm{A}$ and $\mathrm{B}$ is
Find the union of each of the following pairs of sets :
$A=\{1,2,3\}, B=\varnothing$
If $X=\{a, b, c, d\}$ and $Y=\{f, b, d, g\},$ find
$Y-X$
Show that $A \cap B=A \cap C$ need not imply $B = C$
If $X$ and $Y$ are two sets such that $X$ has $40$ elements, $X \cup Y$ has $60$ elements and $X$ $\cap\, Y$ has $10$ elements, how many elements does $Y$ have?