Let A ={1, 2,3, 4}, B = {2, 4, 6}. Then, the number of sets C such that $\mathrm{A}\cap \mathrm{B}\subseteq \mathrm{C}\subseteq \mathrm{A}\cup \mathrm{B}$ is

we have,

$\begin{array}{rl}\mathrm{A}\cap \mathrm{B}& =\{2,4\}\\ \Rightarrow \mathrm{n}(\mathrm{A}\cap \mathrm{B})& =2\\ \mathrm{A}\cup \mathrm{B}& =\{1,2,3,4,6\}\\ \Rightarrow \mathrm{n}(\mathrm{A}\cup \mathrm{B})& =5\\ \mathrm{as} \mathrm{A}\cap \mathrm{B}\subseteq \mathrm{C}\subseteq \mathrm{A}\cup \mathrm{B}& \end{array}$

Set C contains the number of elements 

$=2^{5-2}=2^3=8$