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## Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 1 Set Language Ex 1.4

Question 1.

If P = {1, 2, 5, 7, 9}, Q = {2, 3, 5, 9, 11}, R = {3, 4, 5, 7, 9} and S = {2, 3, 4, 5, 8} then find

(i) (P∪Q)∪R

(ii) (P∩Q)∩S

(m) (Q∩S)∩R

Solution:

P = {1, 2, 5, 7, 9}; Q = {2, 3, 5, 9, 11}; R = {3, 4, 5, 7, 9} and S = {2, 3, 4, 5, 8}

(i) P∪Q = {1, 2, 5, 7, 9} ∪ {2, 3, 5, 9, 11}

= {1, 2, 3, 5, 7, 9, 11}

(P∪Q)∪R = {1, 2, 3, 5, 7, 9, 11} ∪ {3, 4, 5, 7, 9}

= {1, 2, 3, 4, 5, 7, 9, 11}

(ii) P∩Q = {1, 2, 5, 7, 9} ∩ {2, 3, 5, 9, 11}

= {2, 5, 9}

(P∩Q)∩S = {2, 5, 9} ∩ {2, 3, 4, 5, 8}

= (2, 5}

(iii) Q∩S = {2, 3, 5, 9, 11} ∩ {2, 3, 4, 5, 8}

= {2, 3, 5}

(Q∩S)∩R = {2, 3, 5} ∩ {3, 4, 5, 7, 9}

= {3, 5}

Question 2.

Test for the commutative property of union and intersection of the sets

P = {x : x is a real number between 2 and 7} and

Q = {x : x is an irrational number between 2 and 7}

Solution:

P is a real number set

Q is a set of irrational number

∴ Q⊂P

P∪Q= Q∪P = P

∴ Union of sets is commutative.

P∩Q = Q∩P = Q

∴ Intersection of sets is commutative.

Question 3.

If A = {p, q, r, s}, B = {m, n, q, s, t} and C = {m, n, p, q, s}, then verify the associative property of union of sets.

Solution:

When union of sets is associative

A∪(B∪C) = (A∪B)∪C

(B∪C) = {m, n, q, s, t) ∪ {m, n, p, q, s}

= {m, n, p, q, s, t}

A∪(B∪C) = {p, q, r, s} ∪ {m, n, p, q, s, t}

= {m, n, p, q, r, s, t} ……..(1)

(A∪B) = {p, q, r, s} ∪ {m, n, q, s, t}

= {m, n, p, q, r, s, t}

(A∪B)∪C = {m, n, p, q, r, s, t} ∪ {m, n, p, q, s}

= {m, n, p, q, r, s, t} ……….(2)

From (1) and (2) it is verified that A∪(B∪C) = (A∪B)∪C

Question 4.

Verify the associative property of intersection of sets for A = {-11, √2, √5, 7},

B = {√3, √5, 6, 13} and C = {√2, √3, √5, 9}.

Solution:

When intersection of sets is associative

A∩(B∩C) = (A∩B)∩C

(B∩C) = {√3, √5, 6, 13} ∩ {√2, √3, √5, 9}

= {√3, √5}

A∩(B∩C) = {-11, √2, √5, 7} ∩ {√3, √5}

{√5} ………(i)

(A∩B) = {-11, √2, √5, 7} ∩ {√3, √5 ,6, 13}

= {√5}

(A∩B)∩C = {√5} n {√2, √3, √5, 9}

= {√5}……..(2)

From (1) and (2) it is verified that A∩(B∩C) = (A∩B)∩C

Question 5.

If A={ x : x = 2^{n}, n ∈ W and n < 4}, B = {x : x = 2n, n ∈ N and n ≤ 4} and C = {0, 1, 2, 5, 6}, then verify the associative property of intersection of sets.

Solution:

A = {x : x = 2^{n}, n ∈ W and n < 4}

A = {1, 2, 4, 8}

B = {x : x = 2n, n ∈ N and n ≤ 4}

B = {2, 4, 6, 8}

C ={0, 1, 2, 5, 6}

When intersection of sets is associative

A∩(B∩C) = (A∩B)∩C

(B∩C) = {2, 4, 6, 8} ∩ {0, 1, 2, 5, 6}

= {2, 6}

A∩(B∩C)= {1 ,2, 4, 8} ∩ {2, 6}

= {2}……….(1)

(A∩B) = {1, 2, 4, 8} ∩ {2, 4, 6, 8}

= {2, 4, 8}

(A∩B)∩c= {2, 4, 8} n {0, 1, 2, 5, 6}

= {2}………..(2)

From (1) and (2) we get A∩(B∩C) = (A∩B)∩C