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1. Set Operations
(Complement &
Difference of
Sets)

2. At the end of this period,
I can…
• recall union and intersection of sets;
• describe and differentiate complement of
a set and difference of sets;
• determine the region and elements that
belong to each set operation; and
• see the relevance of caring for oneself and
valuing self-respect and self-worth.
Learning
Targets

3. Intersection of Sets (∩)
“COMMON”
Union of Sets (U)
“COMBINE”

4. 1) U = {x|x is a counting number from 1 to 7}
A = {4, 5, 6, 7} B = {6, 7}
Intersection of Sets (∩)
A ∩ B = {6, 7}
Union of Sets (U)
A U B = {4, 5, 6, 7}

5. 2) U = {x|x is a counting number from 1 to 10}
A = {1, 2, 3} B = {4, 5, 6, 7}
Intersection of Sets (∩)
A ∩ B = { }
Union of Sets (U)
A U B = {1, 2, 3, 4, 5, 6, 7}

6. Analyze this illustration and identify the elements that
belong to the following descriptions
What are the elements
that are found in set A
but not in set B?
playstation, television
What are the elements
that are found in set B
but not in set A?
mouse, laptop, speaker
What are the elements in
the Universal Set but
not in set A?
mouse, laptop,
speaker, car
What are the elements in
the Universal Set but
not in set B?
playstation, television,
car

7. Difference of Sets (–)
“Relative Complement”
U = {1, 2, 3, 4, 5, 6, 7, 8, 9,10}
A = {1, 2, 3, 4, 5}
B = {4, 5, 6, 7}
What is A – B?
These are the elements in set A but not in set B.
A – B = {1, 2, 3}
n(A – B) = 3

8. Difference of Sets (–)
U = {1, 2, 3, 4, 5, 6, 7, 8, 9,10}
A = {1, 2, 3, 4, 5}
B = {4, 5, 6, 7}
What if it’s B – A? What will be the
elements of this set and how did you
arrive with the answer?
These are the elements in set B but not in set A.
B – A = {6, 7}
n(B – A) = 2

9. Complement of a Set (’ )
“Complementation”
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 3, 4, 5}
B = {4, 5, 6, 7}
What is A’?
These are the elements in the Universal Set but not in Set A.
A’ = {6, 7, 8, 9, 10}
n(A’) = 5

10. Complement of a Set (’ )
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 3, 4, 5}
B = {4, 5, 6, 7}
What if it’s B’? What will be the
elements of this set and how did
you arrive with the answer?
These are the elements in the Universal Set but not in Set B.
B’ = {1, 2, 3, 8, 9, 10}
n(B’) = 6

11. 1) U = {x|x is a counting
number from 1 to 7}
A = {4, 5, 6, 7}
B = {6, 7}
2) U = {x|x is a counting
number from 1 to 10}
A = {1, 2, 3}
B = {4, 5, 6, 7}
Perform the set operations and find the cardinality of each.
a) A - B = {4, 5}
b) A’ = {1, 2, 3}
c) A - B = {1, 2, 3}
d) A’ = {4,5,6,7,8,9,10}

12. 1) U = {x|x is a counting
number from 1 to 7}
A = {4, 5, 6, 7}
B = {6, 7}
2) U = {x|x is a counting
number from 1 to 10}
A = {1, 2, 3}
B = {4, 5, 6, 7}
Perform the set operations and find the cardinality of each.
e) n(A – B) = 2
f) n(A’) = 3
g) n(A – B) = 3
h) n(A’) = 7

13. CHALLENGE
U = {x|x is a counting number from 1 to 7}
A = {4, 5, 6, 7} B = {6, 7, 4, 5}
What is B’? What is A-B?
B’= { 1,2,3} A-B= { }

14. Set B is a proper
subset of set A
B⊂A
Set A is an improper
subset of set B
A⊆B
Set B is an improper
subset of set A
B⊆A

15. In relation to the lesson today where we
compare the sets to identify its complement
and difference, do you also compare yourself
to others?
Focus on your own strengths and limitations will let you
see your true worth and eventually, be motivated to reach
your dreams and be successful in life

16. Short Quiz 1 on Friday, August 4, 2023
Written Assessment (Next week, check schedule on Gclassroom)
Review the following for the Written Assessment)
Introduction to Sets (Terminologies and Symbols)
Kinds of Sets
Set Operations
Problem Solving Using Venn Diagram (2 & 3 Subsets)
REMINDERS