#self doubt

Question

X $\subseteq$ P(X) is false where as $\left \{x \right \}$$\subseteq$P(X) is true how??

Comments

Basic Points :-

let a set A = {a,b,c}

then what are the subsets ?

1. ∅

2. {a}

3. {b}

4. {c}

5. {a,b}

6. {a,c}

7. {b,c}

8. {a,b,c}

Note that, a is the member of the set, but while you writing subset, you should put it into the set form., i.e., {a}.

 

then what is a powerset ?

collection of all subsets ===> P(A) = { ∅, {a}, {b}, {c}, {a,b}, {a,c}, {b,c}, {a,b,c} }

then {a,b,c} is a member, then subset of this represented as { {a,b,c} } = { A }

 

X ⊆ P(X) is false  ====> X is a set

{X} ⊆ P(X) is true  ====> X is a member