Write ⊆ or ⊄ in the space provided.

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In summary, ⊆ and ⊄ are symbols used in mathematics to show the relationship between two sets. ⊆ represents the subset symbol, indicating that one set is a subset of another, while ⊄ represents the not subset symbol, showing that one set is not a subset of another. These symbols can also be used to express proper subsets, with the symbols ⊂ and ⊊ having the same meaning as ⊆ and ⊄, respectively. The use of these symbols helps to make mathematical expressions more concise and precise. Other related symbols include ⊇, representing the superset symbol, and ⊅, representing the not superset symbol.
  • #1
KOO
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Write ⊆ or in the space provided.

(3,5) _____ [3,5]
[-1,4] ____ (-1,4)
{∅} _____ P(∅)
N * Z ____ Z * NMy Solution)




 
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  • #2
KOO said:
Write ⊆ or in the space provided.

(3,5) _____ [3,5]
[-1,4] ____ (-1,4)
{∅} _____ P(∅)
N * Z ____ Z * NMy Solution)





Hi KOO! :)

The first 2 are correct.

Edit: see Evgeny.Makarov's post for the 3rd.

As for the 4th, can I assume you intended $\mathbb N \times \mathbb Z \underline{\qquad} \mathbb Z \times \mathbb N$?
If so then the left hand side has elements like (1,1) and (1,-1), while the right hand side has elements like (-1,1) and (1,1)...
 
  • #3
I assume the first two questions are about intervals on the real line. Then I agree.

KOO said:
{∅} _____ P(∅)
Note that P(∅) = {∅}.
 
  • #4
Evgeny.Makarov said:
Note that P(∅) = {∅}.

Good point.
Slipped on that one.
 

1. What is the difference between ⊆ and ⊄?

⊆ represents the subset symbol, which means that the set on the left is a subset of the set on the right. ⊄, on the other hand, represents the not subset symbol, indicating that the set on the left is not a subset of the set on the right.

2. How do I use the symbols ⊆ and ⊄ in mathematical expressions?

These symbols can be used in mathematical expressions to show the relationship between two sets. For example, if we have set A = {1, 2, 3} and set B = {1, 2, 3, 4}, we can write A ⊆ B to indicate that all elements of set A are also elements of set B. Similarly, we can write A ⊄ B to show that set A is not a subset of set B.

3. Can I use other symbols to represent subsets?

Yes, there are other symbols that can be used to represent subsets, such as ⊂ and ⊊. These symbols have the same meaning as ⊆ and ⊄, but they are used to show proper subsets, where the sets are not equal.

4. What is the importance of using these symbols in mathematics?

The use of symbols such as ⊆ and ⊄ helps to make mathematical expressions more concise and easier to understand. It also allows for a more precise representation of the relationship between sets.

5. Are there any other related symbols to ⊆ and ⊄?

Yes, there are other symbols that are related to ⊆ and ⊄, such as ⊇ and ⊅. These symbols have the opposite meanings, where ⊇ represents the superset symbol and ⊅ represents the not superset symbol.

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