class lecture notes 8

130 Chapter 7. Logic, Sets, and Counting Techniques (LECTURE NOTES 8)AUAUCCBB(a)Figure 7.1(Venn diagrams: intersection and union)(a) Figure (a), intersection of A and C, A∩C, all elements in both A and C,{x : (x ∈ A) or (x ∈ C)} / {x : (x ∈ A) and (x ∈ C)}(b) Figure (b), union of A and C, A∪C, elements in either A or C,{x : (x ∈ A) or (x ∈ C)} / {x : (x ∈ A) and (x ∈ C)}(c) General intersection.Intersection A 1 ∩A 2 ∩...∩A n equivalent to{x : x belongs to every set }{x : x belongs to at least one of the sets }(d) General union.Union A 1 ∪A 2 ∪...∪A n equivalent to{x : x belongs to every set }{x : x belongs to at least one of the sets }(e) Notation. Often, “∩” dropped, so A∩B becomes AB for example.Consequently, (A∩B)∪(A∩C) equivalent to(AC ′ ) ∪ (BC ′ ) ∪ (AB) / (AB) ∪(AC) / (A ∪ B) ′3. Venn diagrams: difference and complement.(b)AUAUCCBB(a)Figure 7.2(Venn diagrams: difference and complement)(b)