UGC NET CSE | December 2012 | Part 2 | Question: 4

Question

The power set of the set $\{ \Phi \}$ is

• A. $\{ \Phi \}$
• B. $\{ \Phi, \{ \Phi \} \}$
• C. $\{ 0 \}$
• D. $\{ 0, \Phi , \{ \Phi \} \}$

Comments

Video Solution: https://youtu.be/mOfUwNN2JP8?feature=shared&t=1766 

Answer 1

If A is a finite set then set of all subset of A is called power set A denoted by P(A)

Here, A=$\{ \Phi \}$

P(A)=$\{ \Phi, \{ \Phi \} \}$

Hence,Option(B)$\{ \Phi, \{ \Phi \} \}$ is the correct choice.

Comments

Can we define powerset of an element ? If yes, then what will be the powerset of ' Φ ' ?

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@learncp, "Powerset" is defined for a set. Since $\Phi$ is a set (empty set), so we can define $P(\Phi)$ which will be $\{ \Phi \}.$ 

Video Solution: https://youtu.be/mOfUwNN2JP8?feature=shared&t=1766  

Answer 2

Answer: B

let A be any set, then the set of all subsets of A is called power set of A
To understand this question better let’s try to understand it with another example
A = { }
P(A) = {Ф}

A = {a}
P(A) = {Ф, {a}}

A = {a, b}
P(A) = {Ф, {a}, {b}, {a, b}}

A = {Ф}
P(A) = {Ф, {Ф}}

Answer 3

Shouldn't the answer be {o, {}}, where o is the empty set or ϕ

Comments

No options are correct right ??

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Yes, none of the options seem to be correct.

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Option B is correct.. Isnt?

Answer 4

Option B is correct