15.1 Venn Diagrams OBJ: To use Venn diagrams to illustrate intersections and unions of sets.

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Presentation transcript:

15.1 Venn Diagrams OBJ: To use Venn diagrams to illustrate intersections and unions of sets

When drawing a Venn diagram, a rectangle represents the total items counted. Inside the rectangle are circles representing subsets of that total. A B (Page 1: Venn Diagram#1 On Right)

Shade A ∩ B A ∩ B 2, 3 2, 3 3, 4 A B Section 3 (Venn Diagram#3 on Right) A B

Of 1000 Americans, 450 have the antigen A on the surface of their red blood cells and 140 have the antigen B. (Venn Diagram #2 on Right) *****(40 have both)***** 1000 (450) A B (140) 40 What does this represent? A B This is type ___ blood This is type AB blood

Shade A U B (Venn Diagram #4 on Right) 2,3 2,3 3,4 2, 3, 4 A B What does this represent? People that have A or B or both antigen

(Venn Diagram #5 on Right) Shade A ∩ B 2, 3 1,2 What does this represent? A B This is type ___ blood This is type A blood

Of 1000 Americans, 450 have the antigen A on the surface of their red blood cells and 140 have the antigen B (450) A B (140) 410

(Front Page 2: Venn Diagram#1 On Right) Shade A ∩ B 1,4, 3,4 What does this represent? This is type ___ blood This is type B blood

Of 1000 Americans, 450 have the antigen A on the surface of their red blood cells and 140 have the antigen B (450) A B (140) 100

(Venn Diagram #2 On Right) Shade A U B 2, 3, 4 = 1 What does this represent? A B This is type ___ blood This is type 0 blood

Of 1000 Americans, 450 have the antigen A on the surface of their red blood cells and 140 have the antigen B (450) A B (140) 450

(Venn Diagram #2 On Right) Shade A U B 2, 3, 4 = 1 What does this represent? A B This is type ___ blood This is type 0 blood

(Venn Diagram #3 On Right) Shade A ∩ B 1, 4 1, 4 ∩ 1, 2 A B What equation can be written? A U B = A ∩ B

(Venn Diagram #4 On Right) Shade A ∩B 2, 3 2, 3 ∩ 3, 4 3 = 1, 2, 4 AB

(Venn Diagram #5 On Right) Shade A U B 1, 4 1, 4 U 1, 2 1, 2, 4 AB What equation can be written? A ∩ B = A U B

(Back Page 2: Venn Diagram #2 On Right) A ∩ (B U C ) A B C 3, 4, 6, 7 U 5, 6, 7, 8 3, 4, 5, 6, 7, 8 2, 3, 5, 6 ∩ 4, 3, 5, 6, 7, 8 3, 5, 6

B U (A ∩ C ) A B C 1, 4, 7, 8 ∩ 2, 3, 1,4 1, 4, 7, 8 ∩ 2, 3, 1,4 3, 4, 6,7 U 1, 4 1, 3, 4, 6, 7

A ∩ (B ∩ C ) A B

A ∩ (B ∩ C ) A B C 3, 4, 6, 7 ∩ 5, 6, 7, 8 3, 4, 6, 7 ∩ 5, 6, 7, 8 1, 4, 7, 8 ∩ 6, 7 7