COMMUTATIVE PROPERTY OF SET WORKSHEET

Question 1 :

A = {-10, 0, 1, 9, 2, 4, 5} and B = {- 1,- 2, 5, 6, 2, 3, 4}, for the sets A and B, verify that

(i) Set union is commutative. Also verify it by using Venn diagram.

(ii) Set intersection is commutative. Also verify it by using Venn diagram.

Question 2 :

A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6}, for the sets A and B, verify that

(i) set union is commutative. 

(ii) set intersection is commutative. 

Question 3 :

In a group of students 80 can speak Hindi, 60 can speak English and 40 can speak English and Hindi both, then number of students is

a)  100     b)  140       c)  180     d)  60

Question 4 :

If A = {1, 2, 3, 4, 5, 6, 7} and B = {2, 4, 6, 8}, Cardinal number of A - B is 

a)  4     b)  3     c)  9    d)  7

Question 5 :

If A = {1, 2} and B = {3, 4}. Determine the number of relations from A and B.

a)  3     b)  16     c)  5     d)  6

Question 6 :

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

B = {1, 3, 4, 5, 7, 8}

C = {2, 6, 8}, then find (A - B) U C

a)  {2, 6}     b)  {2, 6, 8}     c)  {2, 6, 8, 9}   d)  none

Question 7 :

If A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6 7, 9}, then how many proper subset of A n B can be created ?

1. Answer :

Commutative property :

(i) A u B = B u A

(ii) A n B = B n A

(i) A = {-10, 0, 1, 9, 2, 4, 5} and B = {- 1, -2, 5, 6, 2, 3, 4}

A u B = {-10, 0, 1, 9, 2, 4, 5} u {-1,-2, 5, 6, 2, 3, 4} 

= {-10, -2, -1, 0, 1, 2, 3, 4, 5, 6, 9} ----(1)

B u A = {-1, -2, 5, 6, 2, 3, 4} u {-10, 0, 1, 9, 2, 4, 5}

=  {-10, -2, -1, 0, 1, 2, 3, 4, 5, 6, 9} ----(2)

(1) = (2)

Verifying in Venn diagram :

(ii) A = {-10, 0, 1, 9, 2, 4, 5} and B = {-1,-2, 5, 6, 2, 3, 4}

A n B = {-10, 0, 1, 9, 2, 4, 5} n {-1,-2, 5, 6, 2, 3, 4}

= { 2, 4, 5 } ----(3)

B n A = {-1,-2, 5, 6, 2, 3, 4} n {-10, 0, 1, 9, 2, 4, 5}

= { 2, 4, 5 } ----(4)

(3) = (4)

Verifying in Venn diagram :

2. Answer :

Commutative property :

(i) A u B = B u A

(ii) A n B = B n A

(i) A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6} 

A u B = {1, 2, 3, 4, 5} u {3, 4, 5, 6} 

= {1, 2, 3, 4, 5, 6} ----(5)

B u A = {3, 4, 5, 6} u {1, 2, 3,  4, 5}

= {1, 2, 3, 4, 5, 6} ----(6)

(5) = (6)

(i) A = {1, 2, 3,  4, 5} and B = {3, 4, 5, 6} 

A n B = {1, 2, 3, 4, 5} n {3, 4, 5, 6} 

= {3, 4, 5} ----(7)

B n A =  {3, 4, 5, 6} U {1, 2, 3,  4, 5}

= {3, 4, 5} ----(8)

(7) = (8)

3. Answer :

Let H and E be number of students who speak Hindi and English respectively.

n(HnE) = 40

n(H) = 80

n(E) = 60

n(HUE) = n(H) + n(E) - n(HnE)

= 80 + 60 - 40

= 140 - 40

= 100

So, option a is correct.

4. Answer :

A = {1, 2, 3, 4, 5, 6, 7} and B = {2, 4, 6, 8}

A - B = {1, 3, 5, 7}

n(A - B) = 4

So, option a is correct.

5. Answer :

If A = {1, 2} and B = {3, 4}. Determine the number of relations from A and B.

A = {1, 2}

B = {3, 4}

A x B = {(1, 3) (1, 4) (2, 3) (2, 4)}

n(A x B) = 4

Number of relations from A to B = 2ⁿ

n will be the number of elements from A x B

= 2⁴

= 16

6. Answer :

(A - B) = {1, 2, 3, 4, 5, 6, 7, 8, 9} -  {1, 3, 4, 5, 7, 8}

(A - B) = {2, 6, 9}

(A - B) U C = {2, 6, 9} U {2, 6, 8, 9}

(A - B) U C = {2, 6, 8, 9}

7. Answer :

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

A n B = {2, 4, 7, 9}

n(A n B) = 4

Number of subsets = 2ⁿ

Number of proper subsets = 2ⁿ - 1

= 2⁴ - 1

= 16 - 1

= 15

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