# Venn Diagram Set Notation

Want to learn more about Venn Diagram Set Notation? In this revision note, you will extend your knowledge of Set Language to sketch Venn Diagrams.

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## Venn Diagrams:

A Venn diagram is a pictorial representation of the relationships between sets.

In a Venn diagram, we use a rectangle to denote a universal set U and a loop such as circle or an oval to represent any set in U.

## Venn Diagram Set Notation Example 1

U = { integers x: 1 ≤ x ≤ 28}
A = { x : factor of 27 }
B = { x : multiple of 3 }

(a) Find n ( A ∩ B’ )
(b) On the Venn diagram, shade the region which represent A ∩ B’

Solution
(a) A = {1, 3, 9, 27}
B = {3, 6, 9, 12, 15, 18, 21, 24, 27}

A ∩ B’ = { 1 }
n (A ∩ B’) = 1

(b)

## Venn Diagram Set Notation Example 2

U = { x: x is a positive integer }
A = { x : x ≤ 12 }
B = { x : x > 5 }

(a) List the elements A ∩ B
(b) Find n (B’)
(c) On the Venn diagram, shade the region which represent A ∪ B’

Solution

(a) A = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 }

B = { 6, 7, 8, 9, 10, 11, 12, . . . }

A ∩ B = { 6, 7, 8, 9, 10, 11, 12 }

B’ = { 1, 2, 3, 4, 5 }

(b) n (B‘) = 5

(c)

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