Using set theory
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Using Set Theory. A ~ Set of Students Studying Math B ~ Set of Students Studying History A ∩B ~ The intersection of sets A and B. (Students who study Math and History). S. 2 Sets are disjoint if their intersection is the empty set Ø. Disjoint Sets.

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Using Set Theory

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Using set theory

Using Set Theory

  • A ~ Set of Students Studying Math

  • B ~ Set of Students Studying History

  • A∩B ~ The intersection of sets A and B.

    • (Students who study Math and History)

S


2 sets are disjoint if their intersection is the empty set

2 Sets are disjoint if their intersection is the empty set Ø

  • Disjoint Sets

e.g. if C is the set of students studying grade 10 history and A is the set of students studying grade 12 math there are no grade 10 history students who study grade 12 math.


Using set theory

  • A U B ~ The union of sets A and B, The set of all the elements in either A or B or both


Using set theory

  • n(A) = the number of elements in set A

  • A’ = the set of elements not in A (called A’s compliment)


Union of sets

Union of Sets

  • A U B = {set of element in A or B (or both)}

  • If n(A UB) = n(A) + n(B) the sets are disjoint.


The union of sets generally

The Union of Sets Generally

  • n( A UB) = n( A) + n( B) – n( A∩B )

  • The number of members of set A or B


N a ub n a n b n a b

n( A UB) = n( A) + n( B) – n( A∩B )

  • e.g. A = set of DM Students

    B = set of P.E. Students

    There are 28 DM students and 25 PE students. 12 are in both. How many students in total are in DM or PE (or both)?

    n(A)=28, n(B)=25, n( A∩B )=12

    n( A UB) = n( A) + n( B) – n( A∩B )

    =28 + 25 – 12

    = 41


Example 2

Example 2

Of the 120 students in a class, 30 speak Chinese, 50 speak Spanish, 75 speak French, 12 speak Spanish and Chinese, 30 speak Spanish and French, and 15 speak Chinese and French. Seven students speak all three languages. How many students speaks none of these languages?


Using set theory

7 speak all 3

15 speak Chinese and French

15

30 speak Spanish and French

12 speak Spanish and Chinese

23

5

50 speak Spanish

7

10

30 speak Chinese

37

8

75 Speak French

120 – 105 = 15 don’t speak any.


Homework

Homework

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