Venn Diagrams EQ How do I use a

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Venn Diagrams EQ: How do I use a Venn diagram to represent different sets

Venn Diagrams EQ: How do I use a Venn diagram to represent different sets of numbers and to solve problems?

B A U

B A U

A B U

A B U

A B U

A B U

Disjoint Sets U A B=

Disjoint Sets U A B=

Disjoint and Exhaustive U = {x|-3<x<8, x } A and B are subsets of

Disjoint and Exhaustive U = {x|-3<x<8, x } A and B are subsets of U, A={x|x<5} and B = {x|x 5}

U={1, 2, 3, 4, 5, 6, 7, 8} A = 1, 3, 6, 8

U={1, 2, 3, 4, 5, 6, 7, 8} A = 1, 3, 6, 8 B = {2, 3, 4, 5, 8} A B U

U={1, 2, 3, 4, 5, 6, 7, 8} A = {1, 3, 6, 7,

U={1, 2, 3, 4, 5, 6, 7, 8} A = {1, 3, 6, 7, 8} B = {3, 6, 8} A B U

Four regions on a Venn Diagram 1) In A, but not in B A

Four regions on a Venn Diagram 1) In A, but not in B A B 2) In B, but not in A 3) In both A and B 4) Neither in A nor B U

Example 1 n a) b) c) d) e) f) Given the Venn Diagram below,

Example 1 n a) b) c) d) e) f) Given the Venn Diagram below, how many elements are there in P PUQ Q’ U P, but not Q Q, but not P neither P nor Q? Q P (7) (3) (11) (4)

YOU DO: n a) b) c) d) e) f) Give the number of elements

YOU DO: n a) b) c) d) e) f) Give the number of elements in: X’ X Y XUY X, but not Y Y, but not X Neither X nor Y Y X (8) U (6) (3) (2)

6 + c = 17 ; c = 11 Example 2: 11 8 +

6 + c = 17 ; c = 11 Example 2: 11 8 + 6 + 11 + d = 30 25 + d = 30 ; d = 5 Given n(U) = 30, n(A) = 14, n(B) = 17 and n(A B) = 6 find: a) n(A U B) 25 A b) n(A, but not B) 5 n • b=6 6 8 • a + b = 14 a + 6 = 14 • b + c = 17 a = 8 8 • a + b + c + d = 30 (a) U (b) B (c) (d)

YOU DO: n a) b) c) Given n(U) = 26, n(A) = 11, n(B)

YOU DO: n a) b) c) Given n(U) = 26, n(A) = 11, n(B) = 12 and n(A B) = 8, find: n(A U B) 15 B A n(B, but not A) 4 (a) (c) (b) n(A’) 15 b=8 a + b = 11; a = 3 b + c = 12; c = 4 a + b + c + d = 26 3 + 8 + 4 + d = 26; d = 11 U (d)

Now, the real thing… n A squash club has 27 members. 19 have black

Now, the real thing… n A squash club has 27 members. 19 have black hair, 14 have brown eyes and 11 have both black hair and brown eyes. – Place this information on a Venn Diagram – Find the number of members with: n Black hair or brown eyes n Black hair, but not brown eyes Black (a) (b) (c) Brown a + b + c + d = 27 a + b = 19 a = 8 b + c = 14 c = 3 b = 11 U (d) d=5

YOU DO: Pele has 14 cavies as pets. Five have long hair and 8

YOU DO: Pele has 14 cavies as pets. Five have long hair and 8 are brown. Two are both brown and have long hair. a) Place this information on a Venn diagram b) Find the number of cavies that: a) Are short haired c + d = 9 b) Have short hair and are brown c = 6 c) Have short hair and are not brown d = 3 Long Brown a + b + c + d = 14 d = 3 a+b=5 (a) (b) (c) b+c=8 b=2 U (d) a=3 c=6

A little bit different… n A platform diving squad of 25 has 18 members

A little bit different… n A platform diving squad of 25 has 18 members who dive from 10 m and 17 who dive from 4 m. How many dive from both platforms? 10 m 4 m 1. a + b + c + d = 25 2. a + b = 18 (a) U (b) (c) 3. b + c = 17 (d) 4. 18 + c + 0 = 25 5. c=7 Therefore b + 7 = 17 and b = 10

Now for the real thing… b) A city has three newspapers A, B, and

Now for the real thing… b) A city has three newspapers A, B, and C. Of the adult population, 1% read none of these newspapers, 36% read A, 40% read B, 52% read C, 8% read A and B, 11% read B and C, 13% read A and C and 3% read all three papers. What percentage of the adult population read: Newspaper A only Newspaper B or Newspaper C c) Newspaper A or B but not C n a) A a = 3; a + d = 8; a + b = 11; a + c = 13 Therefore, d = 5, b = 8, and c = 10 d g c g + 3 + 5 + 10 = 36; therefore g = 36 a f e + 3 + 5 + 8 = 40; therefore e = 24 f + 3 + 8 + 10 = 32; f = 31 and h = 1 B U e b C

HW #4 n 4 a – pg 78 #1; #4; pg 79 #7, pg

HW #4 n 4 a – pg 78 #1; #4; pg 79 #7, pg 80 #9 n 4 b – pg 81, 82 #11 - 14

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