Universal Set and Subset using Venn Diagram

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Reference:
Nivera, G. C. (2013), Grade 7 Mathematics: Pattern and Practicalities. Don Bosco Press Inc. Makati City, Philippines.

1. Grade 7 –Mathematics
Quarter I
UNIVERSAL SET
SUBSETSand VENN DIAGRAM

2. •defineuniversalset,subsetand
propersubset;
•illustratesubsetanduniversalset
usingVennDiagram;and
•listallthepossiblesubsetsofagiven
set;

3. Considerthesecards.
Formthefollowingsetsusingthenumbersinthe
cards.
1.A={numberslessthan5}
A={1,2,3,4}
2.B={evennumberslessthan5}
B={2,4}

4. Considerthesecards.
3.C={primenumbers}C={2,3,5,7}
4.D={oddnumbers} D={1,3,5,7,9}
5.E={numbersfrom1to4}E={1,2,3,4}

5. -denotedbyU,containsallthe
elements.
U = {1,2,3,4,5,6,7,8,9,10}

6. 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}

7. Subset
U
Venn Diagram

8. Dogs
Poodles
U
“allpoodlesaredogs”
B⊆A
A
B
U
A={1,2,3}
B={1}
poodles⊆dogs

9. -denotedby⊆,ifandonlyifevery
elementofsetAisalsoanelementof
setB.
-anemptysetisalwaysasubsetof
everyset.

10. -denotedby⊂,ifandonlyifevery
elementofsetAisalsoanelement
ofsetB,andsetBcontainsatleast
oneelementthatisnotinA.
-apropersubsetisalwaysasubset.

11. Example.
{3}_____{1,2,3}⊂
{1,2,3}___{1,2,3}⊆
2___{1,2,3}∈
5___{1,2,3}∉
{7,8}___{1,2,3}⊂
ProperSubset
Subset
NotaSubset
Element
Notanelement

12. Let’sTry!
Fillineachblankwith⊂,⊆,∈,∉,⊂.
1.{2}_____{1,2,3}
2.{g}_____{a,b,c,d,e}
3.4_____{oddnumber}
4.{3,2,1}_____{1,2,3}
5.1_____{1,2,3}
⊆
⊂
∉
⊂
∈

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

14. 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}
16subsets

15. Checking.
�
�
=�
���??????������������
1.{a,b}=4subsets
�
�
=�
�
=2x2
2.{1,2,3}=8subsets
3.{l,o,v,e}=16subsets
�
�
=�
�
=2x2x2
�
�
=�
�
=2x2x2x2