subsets
DESCRIPTION
Subsets Subsets Given sets A and B, set A is a subset of B if every element of A is an element of B. A ⊆ B (A is a subset of B); if and only if X ∈ A, X ∈ B. Superset If A ⊆ B, We may also write B ⊇ A, A is contained in B or B contains A Proper Set If A ⊆ B and A ≠ , if and only if all elements of A belongs to B A ⊂ B, (A is a proper subset of B); if we have the following conditions X ∈ A, X ∈ B. Improper Set But there also exists Y ∈ B such that Y ∉ A. If A ⊆ B and B ⊆ C. If A ⊆ B, then A = B, then A ⊃ B (Ais an improper subset of B) To determine the total number of subsets use the formula 2n where n is the cardinal number F = {4, 5, 6}; n = 3 The subsets of F are { }, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6} Sets No. of Elements No. of Subsets L = {1} 1 2 I = {2, 3} 2 4 F = {4, 5, 6} 3 8 E = {7, 8, 9, 10} 4 16TRANSCRIPT
SUBSETSNicey M
SUBSETS
Given sets A and B, set A is a subset of B if every element of A is an element of B.
A ⊆ B (A is a subset of B); if and only if X ∈ A, X ∈ B.
SUPERSET
If A ⊆ B, We may also write B ⊇ A, A is contained in B or B contains A
PROPER SET
If A ⊆ B and A ≠ , if and only if all elements of A belongs to B
A ⊂ B, (A is a proper subset of B); if we have the following conditions X ∈ A, X ∈ B.
IMPROPER SET
But there also exists Y ∈ B such that Y ∉ A. If A ⊆ B and B ⊆ C. IfA ⊆ B, then A = B, then A ⊃ B (Ais an improper subset of B)
To determine the total number of subsets use the formula 2n where n is the cardinal number
F = {4, 5, 6}; n = 3
The subsets of F are { }, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}
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