Question

Assertion (A) The subsets of the set $\{1,\{2\}\}$ are $\{\},\{1\},\{\{2\}\}$ and $\{1,\{2\}\}$.
Reason (R) The total number of proper subsets of a set containing $n$ elements is $2^n-1$.

• A. Both $A$ and $R$ are correct; $R$ is the correct explanation of $A$
• B. Both $A$ and $R$ are correct; $R$ is not the correct explanation of $A$
• C. $A$ is correct; $R$ is incorrect
• D. $R$ is correct; $A$ is incorrect

Answer 1

Answer: (B)

1 and $\{2\}$ are the element of $\{1,\{2\}\}$
So, the subsets of the set $\{1,\{2\}\}$ are $\varphi ,\{1\},\{\{2\}\}$ and $\{1,\{2\}\}$.
Hence, A is true.
We know, total number of proper subsets of a set containing $n$ elements is $2^n-1$.
Hence, $R$ is true. But $R$ is not the correct explanation of $A$.