Question

Let A = {1, 2, {3, 4}, 5}. Which of the following statements are incorrect and why?

(i) {3, 4} $\subset$ A (ii) {3, 4} $\in$ A

(iii) {{3, 4}} $\subset$ A (iv) $1\in A$

(v) $1\subset A$ (vi) {1, 2, 5} $\subset$ A

(vii) {1, 2, 5} $\in$ A (viii) {1, 2, 3} $\subset$ A

(ix) $\Phi \in A$ (x) $\Phi \subset A$

(xi) {$\Phi$} $\subset$ A.

Answer 1

(i) {3, 4} is a member of set A.

$\therefore$ {3, 4} $\in$ A

Hence {3, 4} $\subset$ A is incorrect.

(ii) {3, 4} is a member of set A.

$\therefore$ {3, 4} $\in$ A is correct.

(iii) Here {3, 4} is a member of set A.

$\therefore$ {{3, 4}} is a set

$\therefore$ {{3, 4}} $\subset$ A is correct.

(iv) 1 is a member of set A.

$\therefore$ $1\in A$ is correct.

(v) 1 is not a set, it is a member of set A.

$\therefore$ $1\subset A$ is incorrect.

(vi) 1, 2, 5 are members of set A.

$\therefore$ {1, 2, 5} is a subset of set A.

$\therefore$ {1, 2, 5} $\subset A$ is correct.

(vii) 1, 2, 5 are members of set A.

$\therefore$ {1, 2, 5} is a subset of set A.

$\therefore$ {1, 2, 5} $\in A$ is incorrect.

(viii) 3 is not a member of set A.

$\therefore$ {1, 2, 3} is not a subset of set A.

$\therefore$ {1, 2, 3} $\subset A$ is incorrect.

(ix) $\Phi$ is not a member of set A.

$\therefore$ $\Phi \in A$ is incorrect.

(x) Since $\Phi$ is subset of every set,

$\therefore$ $\Phi \subset A$ is correct

(xi) $\Phi$ is not a member of set A.

$\therefore$ {$\Phi$} $\subset A$ is incorrect.