Textbook Problem

In each of (a)-(f), answer the following question: Is $A\subseteq B$ ? Is $B\subseteq A$ ? Is either A or B a proper subset of the other?
a. $A=\left\{2,\left\{2\right\},{\left(\sqrt{2}\right)}^2\right\},B=\left\{2,\left\{\left\{2\right\}\right\}\right\}$

b. $A=\left\{3,\sqrt{5^2-4^4},24\mathrm{mod}7\right\},B=\left\{8\mathrm{mod}5\right\}$

c. $A=\left\{\left\{1,2\right\},\left\{2,3\right\}\right\},B=\left\{1,2,3\right\}$

d. $A=\left\{a,b,c\right\},B=\left\{\left\{a\right\},\left\{c\right\}\right\}$

e. $A=\left\{\sqrt{16},\left\{4\right\}\right\}B=\left\{4\right\}$

f. $\begin{array}{l}A=\left\{x\in R|\cos x\in Z\right\},\\ B=\left\{x\in \text{R|}\sin x\in Z\right\}\end{array}$