Let $\text{A, B}$ be two non-empty sets such that $\text{P(A)} \subset \text{P(B)},$ where $\text{P(S)}$ denotes Power set of set $\text{S}$, and $\subset$ denotes “proper subset”. Let $\text{M}$ be the universal set and $\text{A, B}$ are proper subsets of $\text{M}$. For any set $\text{S},$ let $\text{S}'$ be the set of those elements which are in $\text{M}$, but not in $\text{S}.$
Which of the following sets forms a partition of $\text{M}$?
- $\{\text{A} \cap \text{B},\text{A}' \cap \text{B}\}$
- $\{\text{A} \cap \text{B},\text{A}' \cap \text{B},\text{A} \cap \text{B}',\text{A}' \cap \text{B}'\}$
- $\{\text{A} \cap \text{B},\text{A}' \cap \text{B}, \text{A}' \cap \text{B}'\}$
- $\{\text{A} \cap \text{B},\text{A}' \cap \text{B}'\}$
