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## Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 1 Set Language Ex 1.7

Multiple Choice Questions

Question 1.

Which of the following is correct?

(1) {7} ∈ {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

(2) 7 ∈ {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

(3) 7 ∉ {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

(4) {7} ⊈ {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Solution:

(2) 7 ∈ {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Question 2.

The set P = {x | x ∈ Z, -1 < X < 1} is a

(1) Singleton set

(2) Power set

(3) Null set

(4) Subset

Solution:

(1) Singleton set

Hint: P = {0}

Question 3.

If U = {x | x ∈ N, x < 10} and A = {x | x ∈ N, 2 ≤ x < 6} then (A’)’ is

(1) {1, 6, 7, 8, 9}

(2) {1, 2, 3, 4}

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

(4) { }

Solution:

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

Hint: (A’) = A= {2, 3, 4, 5}

Question 4.

If B ⊆ A then n(A ∩ B) is

(1) n(A – B)

(2) n(B)

(3) n(B – A)

(4) n(A)

Solution:

(2) n(B)

Hint: B ⊆ A ⇒ A ∩ B = B

Question 5.

If A= {x, y, z} then the number of non-empty subsets of A is

(1) 8

(2) 5

(3) 6

(4) 7

Solution:

(4) 7

Hint: Number of non-empty subsets = 2 – 1 = 8 – 1 = 7

Question 6.

Which of the following is correct ?

(1) Ø ⊆ {a,b}

(2) Ø ∈ {a, b}

(3) {a} ∈ {a, b}

(4) a ⊆ {a, b}

Solution:

(1) Ø ⊆ {a,b}

Hint: Empty set is an improper subset

Question 7.

If A ∪ B = A ∩ B, then

(1) A ≠ B

(2) A = B

(3) A ⊂ B

(4) B ⊂ A

Solution:

(2) A = B

Question 8.

If B – A is B, then A ∩ B is

(1) A

(2) B

(3) U

(4) Ø

Solution:

(4) Ø

Hint: B – A = B ⇒ A and B are disjoint sets.

Question 9.

From the adjacent diagram n[P(A ∆ B) is

(1) 8

(2) 16

(3) 32

(4) 64

Solution:

(3) 32

Hint: A ∆ B = { 60, 85, 75, 90, 70}

⇒ n(A ∆ B) = 5

⇒ n(P(A ∆ B)) = 2^{5} = 32

Question 10.

If n(A) = 10 and n(B) = 15 then the minimum and maximum number of elements in A ∩ B is

(1) (10, 15)

(2) (15, 10)

(3) (10, 0)

(4) (0, 10)

Solution:

(4) (0, 10)

Question 11.

Let A = {Ø} and B = P(A) then A ∩ B is

(1) {Ø, {Ø} }

(2) {Ø}

(3) Ø

(4) {0}

Solution:

(2) {Ø}

Hint: P(A) = {Ø {Ø}}

Question 12.

In a class of 50 boys, 35 boys play carom and 20 boys play chess then the number of boys play both games is

(1) 5

(2) 30

(3) 15

(4) 10

Solution:

(1) 5

Hint: n(A ∪ B) = n(A) + n(B) – n(A n B) ⇒ 50 = 35 + 20 – n(A ∩ B) ⇒ n(A ∩ B) = 5

Question 13.

If U = {x : x ∈ N and x < 10}, A = {1, 2, 3, 5, 8} and B = {2, 5, 6, 7, 9}, then n[(A ∪ B)’] is

(1) 1

(2) 2

(3) 4

(4) 8

Solution:

(1) 1

Hint: U = {1, 2, 3, 4, 5, 6, 7, 8, 9}

A = {1, 2, 3, 5, 8}

B = {2, 5, 6, 7, 9}

A ∪ B = {1, 2, 3, 5, 6, 7, 8, 9}

(A ∪ B)’ = {4},

n(A ∪ B)’ = 1

Question 14.

For any three sets P, Q and R, P – (Q ∩ R) is

(1), P – (Q ∪ R)

(2) (P ∩ Q) – R

(3) (P – Q) ∪ (P – R)

(4) (P – Q) ∩ (P – R)

Solution:

(3) (P – Q) ∪ (P – R)

Hint: P – (Q ∩ R) = (P – Q) ∪ (P – R)

Question 15.

Which of the following is true?

(1) A – B = A ∩ B

(2) A – B = B – A

(3) (A ∪ B)’ = A’ ∪ B’

(4) (A ∩ B)’ = A’ ∪ B’

Solution:

(4) (A ∩ B)’ = A’ ∪ B’

Hint: (1) (A – B) = A ∩ B ✘

(2) A – B = B – A ✘

(3) (A ∪ B) = A’ ∪ B’ ✘

(4) (A ∩ B)’ = A’ ∪ B’ ✓

Question 16.

If n(A ∪ B ∪ C) = 100, n(A) = 4x, n(B) = 6x, n(C) = 5x, n(A ∩ B) = 20, n(B ∩ C) = 15, n(A ∩ C) = 25 and n(A ∩ B ∩ C)= 10 , then the value of x is

(A) 10

(B) 15

(C) 25

(D) 30

Solution:

(A) 10

Hint:

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(C ∩ A) + n(A ∩ B ∩ C)

100 = 4x + 6x + 5x – 20 – 15 – 25 + 10

100 = 15x -60 + 10

100 = 15x – 50

∴ 15x = 100 + 50 = 150

x = 10

Question 17.

For any three sets A, B and C, (A – B) ∩ (B – C) is equal to

(1) A only

(2) B only

(3) C only

(4) ϕ

Solution:

(4) ϕ

Hint: (A – B) ∩ (B – C) is equal to Φ

Question 18.

If J = Set of three sided shapes, K = Set of shapes with two equal sides and L = Set of shapes with right angle, then J ∩ K ∩ L is

(1) Set of isoceles triangles

(2) Set of equilateral triangles

(3) Set of isoceles right triangles

(4) Set of right angled triangles

Solution:

(3) Set of isoceles right triangles

Hint:

Question 19.

The shaded region in the Venn diagram is

(1) Z – (X ∪ Y)

(2) (X ∪ Y) ∩ Z

(3) Z – (X ∩ Y)

(4) Z ∪ (X ∩ Y)

Answer:

(3) Z – (X ∩ Y)

Hint:

Z – (X ∩ Y)

Question 20.

In a city, 40% people like only one fruit, 35% people like only two fruits, 20% people like all the three fruits. How many percentage of people do not like any one of the above three fruits?

(1) 5

(2) 8

(3) 10

(4) 15

Answer:

(1) 5

Hint:

40 + 35 + 20 + x = 100%

95% + x = 100%

x = 5%