Power Set — IISER Maths MCQs with Solutions
Free IISER Maths Power Set MCQs with step-by-step solutions (4 questions). Part of Sets. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Power Set · medium · theory
For any set $A$, which relation is correct?
A. $A \in P(A)$ ✓ Correct
B. $A \subseteq P(A)$
C. $P(A) \in A$
D. $P(A) \subseteq A$
Solution: $A$ is a subset of itself, so $A$ is a member of its power set: $A \in P(A)$.
Q2 — Power Set · medium · numerical
If $n(P(A)) = 256$, then the number of elements in $A$ is:
A. $16$
B. $7$
C. $128$
D. $8$ ✓ Correct
Solution: $2^{n(A)} = 256 = 2^8 \Rightarrow n(A) = 8$.
Q3 — Power Set · hard · theory
If $A = \{\emptyset, \{\emptyset\}\}$, then the number of elements in $P(A)$ is:
A. $8$
B. $1$
C. $2$
D. $4$ ✓ Correct
Solution: $A$ has 2 elements ($\emptyset$ and $\{\emptyset\}$), so $n(P(A)) = 2^2 = 4$.
Q4 — Power Set · medium · theory
For sets $A \subseteq B$, which relation between their power sets holds?
A. $P(A) = P(B)$
B. $P(A) \subseteq P(B)$ ✓ Correct
C. $P(B) \subseteq P(A)$
D. $P(A) \cap P(B) = \emptyset$
Solution: Every subset of $A$ is also a subset of $B$, so $P(A) \subseteq P(B)$.