GATE 2000
March 18, 2025STQC-NIELIT STA 2021
March 18, 2025GATE 2000
| Question 29 |
Let P(S) denotes the powerset of set S. Which of the following is always true?
| P(P(S)) = P(S) | |
| P(S) ∩ P(P(S)) = {ɸ} | |
| P(S) ∩ S = P(S) | |
| S ∉ P(S) |
Question 29 Explanation:
Let us consider
S={1}
P(S)=[{ }, {1}]
P(P(S)) = [{ }, {1}, {{ }, 1}, {1, { }}]
Option A: P(P(S)) ≠ P(S) (wrong)
Option B: P(S) ∩ P(P(S)) ≠ ɸ (wrong)
Option C: P(S) ∩ S ≠ P(S) (wrong)
Option D: S ∈ P(S) (wrong)
None of the given is correct.
S={1}
P(S)=[{ }, {1}]
P(P(S)) = [{ }, {1}, {{ }, 1}, {1, { }}]
Option A: P(P(S)) ≠ P(S) (wrong)
Option B: P(S) ∩ P(P(S)) ≠ ɸ (wrong)
Option C: P(S) ∩ S ≠ P(S) (wrong)
Option D: S ∈ P(S) (wrong)
None of the given is correct.
Correct Answer: B
Question 29 Explanation:
Let us consider
S={1}
P(S)=[{ }, {1}]
P(P(S)) = [{ }, {1}, {{ }, 1}, {1, { }}]
Option A: P(P(S)) ≠ P(S) (wrong)
Option B: P(S) ∩ P(P(S)) ≠ ɸ (wrong)
Option C: P(S) ∩ S ≠ P(S) (wrong)
Option D: S ∈ P(S) (wrong)
None of the given is correct.
S={1}
P(S)=[{ }, {1}]
P(P(S)) = [{ }, {1}, {{ }, 1}, {1, { }}]
Option A: P(P(S)) ≠ P(S) (wrong)
Option B: P(S) ∩ P(P(S)) ≠ ɸ (wrong)
Option C: P(S) ∩ S ≠ P(S) (wrong)
Option D: S ∈ P(S) (wrong)
None of the given is correct.