May 2024
Intermediate to advanced
687 pages
18h 35m
English
Content preview from Discrete Mathematical Structures by Pearson
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Set Theory 1-7
U
A
A
Thus,
A′ = {x: x ∈ U and x ∉ A}
The shaded part in the Venn diagram represents A′. For example
1. If U = R, then the complement of the set of rational numbers Q say is the set of irrational
numbers.
2. U′ = f and f′ = U.
Note 1.2 The set A - B is also called ‘The complement of B with respect to A’. Further, A - B,
A ∩ B and B - A are disjoint sets.
1.2.9 Laws of Sets
Let A, B and C be any three sets and U the universal set, then
Idempotent Laws: A ∪ A = A and A ∩ A = A
Commutative Laws: A ∪ B = B ∪ A and A ∩ B = B ∩ A
Associative Laws: A ∪ (B ∪ C ) = (A ∪ B) ∪ C and A ∩ (B ∩ C) = (A ∩ B) ∩ C
Distributive Laws: (1) A ∪ (B ∩
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