Question

Let $A=\left\{\varphi ,\left\{\varphi \right\},1,\left\{1,\varphi \right\},2\right\}$. Which of the following are true?
(i) $\varphi \in A$
(ii) $\left\{\varphi \right\}\in A$
(iii) $\left\{1\right\}\in A$
(iv) $\left\{2,\varphi \right\}\subset A$
(v) $2\subset A$
(vi) $\left\{2\left\{1\right\}\right\}\not\subset A$
(vii) $\left\{\left\{2\right\},\left\{1\right\}\right\}\not\subset A$
(viii) $\left\{\varphi ,\left\{\varphi \right\},\left\{1,\varphi \right\}\right\}\subset A$
(ix) $\left\{\left\{\varphi \right\}\right\}\subset A$

Answer 1

(i) True
(ii) True
(iii) False
The correct form would be $\left\{1\right\}\subset A$.
(iv) True
(v) False
The correct form would be 1$\in$A.
(vi) True
(vii) True
(viii) True
(ix) True