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

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In summary, ⊆ is used to represent a subset and ∈ is used to represent an element. $\mathbb{N}$ is a set and it is a subset of ℚ, P(R), and Z. √2 is an element of the set of real numbers, denoted by R.
  • #1
WannaBe
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Question:
Write ⊆ or ∈ in the space provided:
N _______ ℚ
N _______ P(R)
∅ _______ Z
√ 2 _______ R

Solution:
N ∈ ℚ
N ∈ P(R)
∅ ⊆ Z
√ 2 ⊆ R
 
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  • #2
Can you state what $\subseteq$ and $\in$ means?
 
  • #3
MarkFL said:
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.
 
  • #4
Good! :D

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

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

What is the difference between ⊆ and ∈?

⊆ (subset) is used to indicate that a set is a subset of another set, meaning that all elements in the first set are also in the second set. On the other hand, ∈ (element of) is used to show that an element belongs to a set, but not necessarily all elements in the first set are in the second set.

How do I know when to use ⊆ or ∈?

⊆ is used when comparing two sets and determining if one set is a subset of the other. ∈ is used when checking if a single element belongs to a set.

What does {Please Check My Solution} mean?

{Please Check My Solution} is a placeholder for a set. It could represent any set of elements, and the question is asking you to determine if that set is a subset or contains a specific element.

Can I use other symbols besides ⊆ and ∈ to represent subsets and elements?

Yes, there are other symbols that can be used to represent subsets and elements, such as ⊂ (proper subset), ⊈ (not a subset), and ∉ (not an element of). However, ⊆ and ∈ are the most commonly used symbols for these concepts.

Is there a specific order in which I should write the symbols ⊆ or ∈?

No, there is no specific order in which you should write ⊆ or ∈. Both symbols can be written in any order, as long as they are placed correctly in relation to the sets and elements being compared.

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