Question

If $A=\{5,\{5,6\},7\}$, which of the following is correct?

• A. $\{5,6\}\in A$
• B. $\left\{5\right\}\in A$
• C. $\left\{7\right\}\in A$
• D. $\left\{6\right\}\in A$

Answer 1

The correct option is A $\{5,6\}\in A$

If $A=\{5,\{5,6\},7\}$ then the elements of $A$ are $5,\{5,6\},7$

Hence $5\in A,\{5,6\}\in A$ and $7\in A$

Note: $5\ne \left\{5\right\}$

5 is an element of $A$

i.e, $5\in A$

where as $\left\{5\right\}$ is a subset of $A$

i.e, $\left\{5\right\}\subset A$