STANDARD-9 STATE BOARD SAMACHEER BOOK SUBJECT-MATHEMATICS TOPIC: SET LANGUAGE SUB TOPIC: PROPERTIES OF SET OPERATIONS

1. PROPERTIESOFSETOPERATIONS

2. PROPERTIES
OF
SET
OPERATIONS
1. COMMUTATIVE PROPERTY
2. ASSOCIATIVE PROPERTY
3. DISTRIBUTIVE PROPERTY

3. COMMUTATIVE
PROPERTY
 In set language, commutative situations can be seen
when we perform operations.
 For example, we can look into the Union (and
intersection) of sets to find out if the operation is
commutative
 Let A={2,3,8,10} and B={1,3,10,13} be two sets
 Then A∪B ={1,2,3,8,10,13} and B∪A={1,2,3,8,10,13}
 From the above, we see that A∪B=B∪A.
 This is called COMMUTATIVE PROPERTY OF
UNION OF SETS
 Now, A⋂B={3,10} and B⋂A={3,10}.
 Then , we see that A⋂B=B⋂A
 This is called COMMUTATIVE PROPERTY OF
INTERSECTION OF SETS.
(i)Commutative property of union of
sets
(ii)Commutative property of intersection of
sets

4. COMMUTATIVE
PROPERTY
For any two sets A and B
(i) A∪B=B∪A
(ii) A⋂B=B⋂A

5. EXAMPLEFOR
COMMUTATIVE
PROPERTY
If A={b,e,f,g} and B={c,e,g,h}, then verify the
commutative property of (i) union of sets (ii)
intersection of sets.
SOLUTION:
Given A={b,e,f,g} and B={c,e,g,h}
(i)A∪B= {b,c,e,f,g,h} and B∪A={b,c,e,f,g,h}
∴ A∪B=B∪A. It is verified that union of sets
is commutative.
(ii)A⋂B={e,g} and B⋂A={e,g}
∴ A⋂B =B⋂A. It is verified that intersection
of sets is commutative.

6. ASSOCIATIVE
PROPERTY
(i)ASSOCIATIVEPROPERTY
OFUNIONFORSETS
ASSOCIATIVE PROPERTY OF UNION
FOR THREE SETS
Let A={-1,0,1,2}, B={-3,0,2,3} and
C={0,1,3,4} be three sets
Now, B∪C={-3,0,1,2,3,4}
A∪(B∪C)={-3,-1,0,1,2,3,4}………..(1)
Then, A ∪B={-3,-1,0,1,2,3}
(A∪B)∪C={-3,-1,0,1,2,3,4}………..(2)
From (1) and (2), A∪(B∪C)= (A∪B)∪C.
This is associative property of union among
sets A,B and C .

7. ASSOCIATIVE
PROPERTY
(ii)ASSOCIATIVEPROPERTY
OFINTERSECTIONOFSETS
 ASSOCIATIVE PROPERTY OF
INTERSECTION FOR THREE SETS
 Let A={-1,0,1,2}, B={-3,0,2,3} and C={0,1,3,4}
be three sets
 Now, B⋂C={0,3}
 A⋂( B⋂C) ={0}……………(3)
 A⋂ B={0,2}
 (A⋂ B)⋂C={0}……………..(4)
 From (3) and (4) A⋂( B⋂C) = (A⋂ B)⋂C
 This is associative property of intersection
among sets A,B and C.

8. ASSOCIATIVE
PROPERTY
For any three sets A,B and C
(i)A∪(B∪C)= (A∪B)∪C
(ii)A⋂( B⋂C) = (A⋂ B)⋂C

9. EXAMPLEOF
ASSOCIATIVE
PROPERTY
={m,n,p,q,s}, then verify the Associative
property of union of sets.
SOLUTION:
Given A={p,q,r,s} ,B={m,n,q,s,t} and
C={m,n,p,q,s}
ASSOCIATIVE PROPERTY OF UNION OF
SETS
 For any three sets A,B and C
A∪(B∪C)= (A∪B)∪C
B∪C={m,n,p,q,s,t}
A∪(B∪C)= {m,n,p,q,r,s,t}………..(1)
A∪B={m,n,p,q,r,s,t}
(A∪B)∪C ={m,n,p,q,r,s,t}………….(2)
From (1) and (2) we get A∪(B∪C)= (A∪B)∪C
This is verified that union of sets is

10. DISTRIBUTIVE
PROPERTY
DISTRIBUTIVE PROPERTY:
For any three sets A,B and C
(i)A⋂(B∪C)=(A ⋂B) ∪(A ⋂C)
[Intersection over Union]
(ii)A ∪(B ⋂C)=(A ∪ B) ⋂(A ∪C)
[Union over Intersection]

11. EXAMPLEFOR
DISTRIBUTIVE
PROPERTY
 If A={0,2,4,6,8}, B={ x : x is a prime number
and x ≺ 11} and C= { x : x ∈ N and 5≤ x≺9 then
verify A ∪(B ⋂C)=(A ∪ B) ⋂(A ∪C)
 SOLUTION:
Given A={0,2,4,6,8}, B={2,3,5,7} and C= {5,6,7,8}
B ⋂C={5,7}
A ∪(B ⋂C)={0,2,4,5,6,7,8}……….(1)
A ∪ B ={0,2,3,4,5,6,7,8}
A ∪C={0,2,4,5,6,7,8}
(A ∪ B) ⋂(A ∪C)= {0,2,4,5,6,7,8}……….(2)
From (1) and (2) we get A ∪(B ⋂C)=(A ∪ B) ⋂(A ∪C)
Hence, it is verified.

12. THANKYOU