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1. MATHEMATICS IN THE
MODERN WORLD
Learning Plan

2. SET THEORY

3. LET’S REVIEW
• WHAT ARE THE THREE METHODS OF SPECIFYING SETS?
• WHAT IS AN INFINITE SET?
• IT IS THE NUMBER OF ELEMENT/S INSIDE THE SET.
• IT IS THE COMPLETE LIST OR THE TOTALITY OF ALL THE
ELEMENTS.
• ENUMERATE THE OPERATIONS ON SET THEORY.

4. LET’S REVIEW
ARE THE FOLLOWING EQUIVALENT?.
• A= {1,2,3,4,5}
• B={3,2,4,6,7}
• A={EGG,BUTTER,BREAD}
• B={GOAT,PIG,DOG}
• A={x|x ∈ positive integers less than 9}
• B={x|x ∈ positive integers less than 9}

5. LET’S REVIEW
• DETERMINE ALL THE POSSIBLE SUBSETS OF THE FF.
• PERFORM THE OPERATION OF SETS.
• U={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}
• A={x|x∈ even positive integers less than 12}
• B={1,2,3,6,7,9,12}
• C={4,6,7,10,11,17,20}
• D={x|x ∈ positive integers less than 20 & multiples of 3}
• E={x|x ∈ positive integers less than 16 divisible by 3}

6. LET’S REVIEW
• Given that n(U)=50, n(A)=25 and n(B)=20
1. Find the greatest value of n(A∩B)
2. Find the least value of n(A∩B)
3. Find the greatest value of n(A∪B)
4. Find the least value of n(A∪B)

7. LET’S REVIEW
• The HAIR Company offers two brands of shampoo:
brand H and brand S, 100 people were surveyed and
their brand preferences are as follows:
• 50 people like brand H.
• 35 people like brand S.
1. What is the maximum number if people who like both
H and S?
2. …minimum of people who like both H and S?
3. …minimum of people whodo not like any of the
brands?

8. LET’S REVIEW
• VENN DIAGRAM
are very useful in showing the relationship U between
sets. The Venn diagram which consists of a rectangle
represents the universal set and a circle or circles inside
the rectangle to represent the set or sets being
considered in the discussion.

9. WORD PROBLEMS
Out of 50 students, 20 are members of Math Club and 36
are members of Glee Club. If 12 are in both clubs, how
many students are in a) neither of the clubs and b) either
of the clubs?

10. WORD PROBLEMS
In a batch of 250 students, 62 are members of Sports
Club, 170 students are members of Drama Club, and 40
students are in both clubs. How many students are:
a. In either the Sports Club or Drama Club?
b. In neither of the clubs?

11. WORD PROBLEMS
A class adviser surveys 35 of his students on the kind of
pets they have at home. He found that 15 have dogs, 12
have cats, and 8 have birds. Five have dogs and cats, 4
have dogs and birds, and 2 have cats and birds. If no one
has all three kinds of pets, how many students have none
of these pets?

12. WORD PROBLEMS
In Mrs. Cruz’s advisory class with 30 students, 20 like
Mathematics. 15 like English, and 6 don’t like
Mathematics or English. How many students like both
Mathematics and English?

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