Prove that $A\subset \varphi \Rightarrow A=\varphi$.

Write down all the subsets of $A=\left\{1,2,3\right\}$. What is the power set in this case? Write down the proper subsets of $A$.

What is the total number of all subsets of a set A containing $8$ elements?

Check whether the following statement is correct and why?

Let $A=\left\{1, 2, \left\{3, 4\right\}, 5\right\}$, then $\left\{3, 4\right\}\subset A$

Check whether the following statement is correct and why?

Let $A=\left\{1, 2, \left\{3, 4\right\}, 5\right\}$, then $\left\{3,4\right\}\in A$

Check whether the following statement is correct and why?

Let $A=\left\{1, 2, \left\{3, 4\right\}, 5\right\}$, then $\left[\left\{3,4\right\}\right]\subset A$

Check whether the following statement iscorrect and why?

Let $A=\left\{1, 2, \left\{3, 4\right\}, 5\right\}$, then $1\in A$

Check whether the following statement is correct and why?

Let $A=\left\{1, 2, \left\{3, 4\right\}, 5\right\}$, then $1\subset A$

State whether the following statement is true or false :

Let $A=\left\{1, 2, \left\{3, 4\right\}, 5\right\}$, then $\left\{1, 2, 5\right\}\subset A$