Question:
Which of the following statements are correct?
Write a correct form of each of the incorrect statements.
(i) $a \subset\{a, b, c\}$
(ii) $\{a\} \in\{a, b, c\}$
(iii) $a \in\{\{a\}, b\}$
(iv) $\{a\} \subset\{\{a\}, b\}$
(v) $\{b, c\} \subset\{a,\{b, c\}\}$
(vi) $\{a, b\} \subset\{a,\{b, c\}\}$
(vii) $\phi \in\{a, b\}$
(viii) $\phi \subset\{a, b, c\}$
(ix) $\{x: x+3=3\}=\phi$
Solution:
Here, (viii) is correct.
The correct forms of each of the incorrect statements are:
(i) $a \in\{a, b, c\}$
(ii) $\{a\} \subset\{a, b, c\}$
(iii) $\{a\} \in\{\{a\}, b\}$
(iv) $\{\{a\}\} \subset\{\{a\}, b\}$
(v) $\{b, c\} \in\{a,\{b, c\}\}$
(vi) $\{a, b\} \not \subset\{a,\{b, c\}\}$
(vii) $\phi \subset\{a, b\}$
(ix) $\{x: x+3=3\} \neq \phi$