Which of the following statements are correct?

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) $\{x: x+3=3\} \neq \phi$

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