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Set Notations and Their Representations
Set notation is a way of representing a set of numbers or objects. The following set notations represent different relationships between two sets A and B, and an element x.
1. A ⊂ B (A is a proper subset of B)
This set notation means that all elements in set A are also present in set B, but set B may have more elements than set A. In other words, A is a subset of B, but not equal to B.
2. x ∉ A (x is not an element of A)
This set notation means that x is not present in set A.
3. A ⊃ B (A contains B)
This set notation means that all elements in set B are also present in set A. In other words, A is a superset of B.
4. {0} (singleton with an only element zero)
This set notation represents a singleton set, which contains only one element, zero.
5. A ⊂ B and x ∈ A (A is a proper subset of B and x is an element of A)
This set notation means that A is a subset of B, but not equal to B, and x is present in set A.
6. A ⊆ B (A is contained in B)
This set notation means that all elements in set A are also present in set B. In other words, A is a subset of B or equal to B.
7. A ⊂ B and {0} ∈ A (A is a proper subset of B and A contains zero)
This set notation means that A is a subset of B, but not equal to B, and A contains the element zero.
8. A ⊂ B and A ∩ B = ∅ (A is a proper subset of B and A does not contain B)
This set notation means that A is a subset of B, but not equal to B, and A does not have any elements in common with B.
Therefore, option A correctly represents the relationship between sets A and B, where A is a proper subset of B.
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