Universal Set and Subset using Venn Diagram

Grade 7 – Mathematics
Quarter I
UNIVERSAL SET
SUBSETS and VENN DIAGRAM

•define universal set, subset and
proper subset;
•illustrate subset and universal set
using Venn Diagram; and
•list all the possible subsets of a given
set;

Consider these cards.
Form the following sets using the numbers in the
cards.
1. A = {numbers less than 5}
A = {1,2,3,4}
2. B = {even numbers less than 5}
B = {2,4}

Consider these cards.
3. C = {prime numbers} C = {2,3,5,7}
4. D = {odd numbers} D = {1,3,5,7,9}
5. E = {numbers from 1 to 4} E = {1,2,3,4}

- denoted by U, contains all the
elements.
U = {1,2,3,4,5,6,7,8,9,10}

U = {1,2,3,4,5,6,7,8,9,10}
A = {1,2,3,4}
B = {2,4}
C = {2,3,5,7}
D = {1,3,5,7,9}
E = {1,2,3,4}

Dogs
Poodles
U “all poodles are dogs”
B⊆A
A
B
U A = { 1, 2, 3 }
B = { 1 }
poodles ⊆ dogs

- denoted by ⊆, if and only if every
element of set A is also an element of
set B.
- an empty set is always a subset of
every set.

- denoted by ⊂, if and only if every
element of set A is also an element
of set B, and set B contains at least
one element that is not in A.
- a proper subset is always a subset.

Example.
{3} _____ {1,2,3}⊂
{1,2,3} ___ {1,2,3}⊆
2 ___ {1,2,3}∈
5 ___ {1,2,3}∉
{7, 8} ___ {1,2,3}⊂
Proper Subset
Subset
Not a Subset
Element
Not an element

Let’s Try!
Fill in each blank with ⊂, ⊆, ∈, ∉, ⊂.
1. {2} _____ {1,2,3}
2. {g} _____ {a,b,c,d,e}
3. 4 _____ {odd number}
4. {3,2,1} _____ {1,2,3}
5. 1 _____ {1,2,3}
⊆
⊂
∉
⊂
∈

NUMBER OF SUBSETS
2. {1,2,3}
{ }
{1}, {2}, {3}
{1,2}, {2,3}, {1,3}
{1,2,3}
8 subsets
1. {a,b}
{ }
{a}, {b}
{a,b}
4 subsets

3. {l,o,v,e}
{ }
{l}, {o}, {v}, {e}
{l,o}, {l,v}, {l,e}, {o,v}, {o,e}, {v,e}
{l,o,v}, {l,o,e}, {l,v,e}, {o,v,e}
{l,o,v,e}
16 subsets

Checking.
𝟐 𝒏
= 𝟐 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒆𝒍𝒆𝒎𝒆𝒏𝒕𝒔
1. {a,b} = 4 subsets
𝟐 𝒏
= 𝟐 𝟐
= 2 x 2
2. {1,2,3} = 8 subsets
3. {l,o,v,e} = 16 subsets
𝟐 𝟑
= 𝟐 𝟑
= 2 x 2 x 2
𝟐 𝟒
= 𝟐 𝟒
= 2 x 2 x 2 x 2

Universal Set and Subset using Venn Diagram

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Universal Set and Subset using Venn Diagram