Write ⊆ or ∈ in the space provided: {Please Check My Solution}

[WannaBe]

Question:
Write ⊆ or ∈ in the space provided:
N _______ ℚ
N _______ P(R)
∅ _______ Z
√ 2 _______ R

Solution:
N ∈ ℚ
N ∈ P(R)
∅ ⊆ Z
√ 2 ⊆ R

 

[MarkFL]

Can you state what $\subseteq$ and $\in$ means?

 

[WannaBe]

Can you state what $\subseteq$ and $\in$ means?

⊆ = Subset
∈ = Element

Definition:

If all the elements of a set is contained in ANOTHER set, then the set whose elements are contained in another set is a subset.
Ex. Set A 's elements= 1,2,3 Set B's elements= 1,2,3,4,5 so... that means all the elements of Set A are in Set B, so A ⊆ B.

 

[MarkFL]

Good!

So, in reference to the first part of the question, is $\mathbb{N}$ a set or an element?