Question

Let $A=\{1,\left\{2\right\},\{3,4\},5\}$. Which of the following are incorrect statements?
Rectify each:

$\left(i\right)2ϵA$

$\left(ii\right)\left\{2\right\}\subset A$

$\left(iii\right)\{1,2\}\subset A$

$\left(iv\right)\{3,4\}\subset A$

$\left(v\right)\{1,5\}\subset A$

$\left(vi\right)\left\{\varphi \right\}\subset A$

$\left(vii\right)1\subset A$

$\left(viii\right)\{1,2,3,4\}\subset A$

Answer 1

Clearly, A contains four elements, namely $1,\left\{2\right\},\{3,4\}$ and 5

(i) $2ϵA$ is incorrect, The correct satement would be $\left\{2\right\}ϵA$.

(ii) $\left\{2\right\}\subset A$ is incorrect. The correct statement is $\left\{\left\{2\right\}\right\}\subset A$

(iii) Clearly, $2\notin A$and therefore, $\{1,2\}\subset A$ is incorrect. The correct statement would be $\{1,\left\{2\right\}\}\subset A$.

(iv) Clearly, $\{3,4\}$ is an element of A.
So, $\{3,4\}\subset A$ is incorrect and $\left\{\{3,4\}\right\}\subset A$ is correct.

(v) Since 1 and 5 are both elements of A, so $\{1,5\}\subset A$ is correct.

(vi) Since $\varphi \notin A$, so $\left\{\varphi \right\}\subset A$ is incorrect while $\left\{\varphi \right\}\subset A$ is correct.

(vii) Since $1ϵA$, so $1\subset A$ is incorrect and therefore, $\left\{1\right\}\subset A$ is correct.

(viii) Since $2\notin A$ and $3\notin A$, so $\{1,2,3,4\}\subset A$ is incorrect.
The correct statement would be $\{1,\left\{2\right\},\{3,4\}\}\subset A$