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OPERATION ON SET

GRADE 7 MATHEMATICS QUARTER I

Objectives:

define and describe the union and intersection of sets;
illustrate difference of two sets and complement of a set; and
use Venn Diagram to represent set operations.

INTERSECTION OF SETS

The intersection of sets A and B, written A ∩ B, is the set containing the elements that are in both A and B.

EXAMPLE:

EXAMPLE 1: INTERSECTION OF SETS

Example:

A = {1, 3, 5, 7, 9}

B = { 2, 3, 5, 7, 11}

A ∩ B = {3, 5, 7} * common elements

It is also called JOINT SETS since both A and B have a common elements which is 3, 5, 7.

VENN DIAGRAM

EXAMPLE 2: INTERSECTION OF SETS

Example:

A = {1, 3, 5, 7, 9}

B = { 2, 4, 6, 8, 10}

A ∩ B = { } *the intersection of both A and B is an empty set since there is no common elements

It is also called DISJOINT SETS since both A and B have a NO common elements.

VENN DIAGRAM

UNION OF SETS

The union of sets A and B, written A ∪ B, is the set of all the elements that are in A, or in both A and B.

EXAMPLE 1: UNION OF SETS

Example:

A = {1, 3, 5, 7}

B = { 1, 2, 3, 4}

A ∩ B = {1, 2, 3, 4, 5, 7} * combining elements

It is also called JOINT SETS since both A and B have a common elements which is 3, 5, 7.

VENN DIAGRAM

ACTIVITY: INTERSECTION AND UNION OF SETS

LETS TRY!

A = {1, 3, 5, 7}

B = {2, 3, 5, 7}

C = {2, 4, 6, 8}

D = {2, 3, 4, 5}

A ∩ B =?
A ∪ B =?
A ∩ C =?
C ∩ D =?
B ∪ D =?

You may answer this via Gforms link:https://forms.gle/gDy3dWiyd8bTNcdXA

COMPLIMENT OF A SET

The complement of a set, written A' , is the set of elements in the universal set that are not in A.

EXAMPLE 1:

COMPLEMENT OF A SET A

Example: U = {1, 2, 3, 4, 5}

A' = {2, 4}

B '= { 2, 3, 4}

C' = {1, 2, 3, 4, 5}

D' = { }

A' = {1, 3, 5}

B' = {1, 5}

C' = { }

D' = {1, 2, 3, 4, 5}

A' = {1, 3, 5}

B' ={ 1, 5}

C' = { }

B' ={ 1, 2, 3, 4, 5}

DIFFERENCE OF TWO SETS

The difference of set A and B, written as A – B, is a set of elements in A that are not in B.

EXAMPLE 1: DIFFERENCE OF TWO SETS

If A = {1, 2, 3} and B = {1, 2, 4, 5, 6}, then A – B = {3} while, B – A = {4, 5, 6}.
If A = {a, b, c, d, e} and B = {a, e, i, o, u}, then A – B = {b, c, d}, while B – A = {i, o, u}.
If A = {Monday, Tuesday, Wednesday, Thursday, Friday} and B = {Saturday, Sunday}, then A – B = {Monday, Tuesday, Wednesday, Thursday, Friday} while B – A = {Saturday, Sunday}.

EXAMPLE 2: DIFFERENCE OF TWO SETS

GIVEN:

A = {1, 2, 4, 5}

B = {2, 3, 5}

C = {1, 3, 5)

D = {2, 4, 5}

A - B = ?
B - A = ?
A - C = ?
C - D = ?
D - A = ?

ANSWER:

A - B = {1, 4}
B - A = {3}
A - C = {2, 4}
C - D = {1, 3}
D - A = { }

TEST YOUR KNOWLEDGE!

PERFORM THE FOLLOWING OPERATIONS ON SETS

Given:

A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

B = {2, 4, 6, 8, 10}

C = {1, 3, 5, 7, 9}

1. A ∩ C = ?

2. B ∩ C = ?

3. A 𝖴 B = ?

4. B 𝖴 C = ?

5. A – C = ?

6. B – C = ?

You may answer this via Gforms link: https://forms.gle/exQkam77r4i93YH47

VIDEO LESSON FOR BETTER UNDERSTANDING:

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