Improper subset | proper subset | Set | Subsets | super set
Subsets | Proper subset | Improper subset | Super set
SUBSETS
Let A and B be two sets. If every element of A is an element of B, then A is called a subset of B and B is called super set of A.
A ⊆ B is read as A is subset of B
B ⊃ A is read as B is super set of A
Thus A ⊆ B
a ∈ A ⇒ a ∈ B
The symbol “⇒” stands for implies.
PROPER SUBSET
A subset A of a set B is called proper set of B if A ≠ B and we write A ⊂ B
IMPROPER SUBSET
A subset A of a set B is called improper set of B if A = B
Example
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{ 1} ⊆ { 1, 2, 3 }, but {1, 4} ⊄ { 1, 2, 3}
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N ⊂ Z ⊂ Q ⊂ R ⊂ C , Where N, Z, Q, R, and C have their usual meanings
NOTE
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Every set is a subset of itself
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The empty set is subset of every set
NOTE THIS POINT
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If A is a proper subset of B, then there exists an element x ∈ B such that x ∈ A
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Two set A and B are equal if A ⊆ B and B ⊆ A then A = B.
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Symbol “ ⊆ “ is denote either subset is proper or improper.
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