What is the Power Set of {a,b} in Relation to Subsets?

[flyingpig]

Homework Statement

Let A = {a,b}, find P(A), the power set which contains all subsets of A

Soln:

P(A) = {empty set, {a}, {b}, {a,b}}

Why is {a,b} in there? Isn't that an element? Shouldn't it be {{a,b}}

So

P(A) = {es, {a}, {b}, {{a,b}}}?

 

[gb7nash]

Let A = {a,b}, find P(A), the power set which contains all subsets of A

Soln:

P(A) = {empty set, {a}, {b}, {a,b}}

Why is {a,b} in there? Isn't that an element?

Yes. {a,b} is an element of P(A). That is, the set consisting of a and b is an element. Likewise, the set consisting of a is an element, the set consisting of b is an element.

 

[Tomer]

No, why?
A is a subset of B if and only if $A\subseteq B$.
Since {a,b} = {a,b} (do you agree? ), {a,b}$\subseteq${a,b}, and therefore, {a,b} is a subset of {a,b}.

(that is of course true generally: $A\subseteq A$ so $A\in P(A)$)

However, {{a,b}} doesn't hold this relation.

 

[vela]

The set A has two elements, a and b. That's it.

{a}, {b}, and {a,b} are subsets of A, not elements of A.

 

[flyingpig]

(that is of course true generally: $A\subseteq A$ so $A\in P(A)$)

Yeah not following that logic at all lol

 

[Tomer]

Yeah not following that logic at all lol

What aren't you following?

 

[flyingpig]

You know what, I got confused with another problem with this one. That problem had 1 nonset element and all the others are.

Thank you everyone