Example 2 3 4 5

Dear Student

$$\begin{gathered} Given \\ A=\{a,b,c,d\} B=\{a,b,c] and C=\{b,d\} \\ P\left(A\right)=\{\varnothing ,\{a\},\{b\},\{c\},\{d\},.......\} \\ P\left(B\right)=\{\varnothing ,\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\},\{a,b,c\left\}\right\} \\ P\left(C\right)=\{\varnothing ,\{b\},\{d\},\{b,d\left\}\right\} \\ \left(i\right)Now X\subset B and X\subset C \\ \Rightarrow X\in P\left(B\right) and X\in P\left(C\right) \\ \Rightarrow X\in \left\{\varnothing ,\left\{b\right\}\right\} \\ \Rightarrow X=\left\{\varnothing ,\left\{b\right\}\right\} \\ \left(ii\right)X\subset A and X is not a subset ofB \\ \Rightarrow X\in P\left(A\right) and X\notin P\left(B\right) \\ \Rightarrow X=\left\{\left\{d\right\},\left\{a,d\right\},\left\{b,d\right\},\left\{c,d\right\},\left\{a,b,d\right\},\left\{b,c,d\right\},\left\{a,c,d\right\},\left\{a,b,c,d\right\}\right\} \end{gathered}$$
Kindly request you to post the other questions in different thread
Regards