Question

Which of the following statements are correct?
Write a correct form of each of the incorrect statements.
(i) $a\subset \left\{a,b,c\right\}$
(ii) $\left\{a\right\}\in \left\{a,b,c\right\}$
(iii) $a\in \{\left\{a\right\},b\}$
(iv) $\left\{a\right\}\subset \left\{\left\{a\right\},b\right\}$
(v) $\left\{b,c\right\}\subset \left\{a,\left\{b,c\right\}\right\}$
(vi) $\left\{a,b\right\}\subset \left\{a,\left\{b,c\right\}\right\}$
(vii) $\varphi \in \left\{a,b\right\}$
(viii) $\varphi \subset \left\{a,b,c\right\}$
(ix) $\left\{x:x+3=3\right\}=\varphi$

Answer 1

Here, (viii) is correct.

The correct forms of each of the incorrect statements are:
(i) $a\in \left\{a,b,c\right\}$
(ii) $\left\{a\right\}\subset \left\{a,b,c\right\}$
(iii) $\left\{a\right\}\in \{\left\{a\right\},b\}$
(iv) $\left\{\left\{a\right\}\right\}\subset \left\{\left\{a\right\},b\right\}$
(v) $\left\{b,c\right\}\in \left\{a,\left\{b,c\right\}\right\}$
(vi) {a,b}⊄{a,{b,c}}
(vii) $\varphi \subset \left\{a,b\right\}$
(ix) $\left\{x:x+3=3\right\}\ne \varphi$