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NCERT solution class 11 chapter 1 Sets exercise 1.5 mathematics

EXERCISE 1.5


Page No 20:

Question 1:

Let U ={1, 2, 3; 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find

(i) 

(ii) 

(iii) 

(iv) 

(v) 

(vi) 

Answer:

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

A = {1, 2, 3, 4}

B = {2, 4, 6, 8}

C = {3, 4, 5, 6}

(i) 

(ii) 

(iii) 

(iv) 

(v) 

(vi) 

Question 2:

If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:

(i) A = {a, b, c}

(ii) B = {d, e, f, g}

(iii) C = {a, c, e, g}

(iv) D = {fgha}

Answer:

U = {a, b, c, d, e, f, g, h}

(i) A = {a, b, c}

(ii) B = {d, e, f, g}

(iii) C = {a, c, e, g}

(iv) D = {fgha}

Question 3:

Taking the set of natural numbers as the universal set, write down the complements of the following sets:

(i) {xx is an even natural number}

(ii) {xx is an odd natural number}

(iii) {xx is a positive multiple of 3}

(iv) {xx is a prime number}

(v) {xx is a natural number divisible by 3 and 5}

(vi) {xx is a perfect square}

(vii) {xx is perfect cube}

(viii) {xx + 5 = 8}

(ix) {x: 2x + 5 = 9}

(x) {xx ≥ 7}

(xi) {xx ∈ N and 2x + 1 > 10}

Answer:

U = N: Set of natural numbers

(i) {xx is an even natural number}´ = {xx is an odd natural number}

(ii) {xx is an odd natural number}´ = {xx is an even natural number}

(iii) {xx is a positive multiple of 3}´ = {xx ∈ N and x is not a multiple of 3}

(iv) {xx is a prime number}´ ={xx is a positive composite number and x = 1}

(v) {xx is a natural number divisible by 3 and 5}´ = {xx is a natural number that is not divisible by 3 or 5}

(vi) {xx is a perfect square}´ = {xx ∈ N and is not a perfect square}

(vii) {xx is a perfect cube}´ = {xx ∈ N and is not a perfect cube}

(viii) {xx + 5 = 8}´ = {xx ∈ N and x ≠ 3}

(ix) {x: 2x + 5 = 9}´ = {xx ∈ N and x ≠ 2}

(x) {xx ≥ 7}´ = {xx ∈ N and x < 7}

(xi) {xx ∈ N and 2x + 1 > 10}´ = {xx ∈ N and ≤ 9/2}

Question 4:

If U = {1, 2, 3, 4, 5,6,7,8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that

(i)  (ii) 

Answer:

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

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

(i)

(ii)

Question 5:

Draw appropriate Venn diagram for each of the following:

(i) 

(ii) 

(iii) 

(iv) 

Answer:

(i) 

(ii) 

(iii) 

(iv) 

Question 6:

Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is?

Answer:

is the set of all equilateral triangles.

Page No 21:

Question 7:

Fill in the blanks to make each of the following a true statement:

(i) 

(ii) Φ′ ∩ A = …

(iii) 

(iv) 

Answer:

(i) 

(ii) Φ′ ∩ A = U ∩ A = A

∴ Φ′ ∩ A = A

(iii) A ∩ A′ = Φ

(iv) U′ ∩ A = Φ ∩ A = Φ

∴ U′ ∩ A = Φ


 

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