NCERT Solutions for Class 11 Maths Chapter 1 – Sets Ex 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) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_m2c2c56cf.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_m2c2c56cf.gif)
(ii) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_670d53cf.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_670d53cf.gif)
(iii) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_65970ef7.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_65970ef7.gif)
(iv) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_dc5f1d8.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_dc5f1d8.gif)
(v) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_m642041a0.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_m642041a0.gif)
(vi) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_67a0793.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_67a0793.gif)
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) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_5c71f8ac.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_5c71f8ac.gif)
(ii) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_33c905a2.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_33c905a2.gif)
(iii) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_m7af1fd34.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_m7af1fd34.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_m44768f0f.gif)
(iv) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_m352d6372.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_m352d6372.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_m383a96e9.gif)
(v) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_m1bf6a326.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_m1bf6a326.gif)
(vi) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_1108c5b6.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_1108c5b6.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3934/CHAPTER%201_html_m53bc8634.gif)
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 = {f, g, h, a}
Answer:
U = {a, b, c, d, e, f, g, h}
(i) A = {a, b, c}
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3935/CHAPTER%201_html_45eed361.gif)
(ii) B = {d, e, f, g}
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3935/CHAPTER%201_html_m747379fd.gif)
(iii) C = {a, c, e, g}
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3935/CHAPTER%201_html_m672caf91.gif)
(iv) D = {f, g, h, a}
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3935/CHAPTER%201_html_430a2659.gif)
Question 3:
Taking the set of natural numbers as the universal set, write down the complements of the following sets:
(i) {x: x is an even natural number}
(ii) {x: x is an odd natural number}
(iii) {x: x is a positive multiple of 3}
(iv) {x: x is a prime number}
(v) {x: x is a natural number divisible by 3 and 5}
(vi) {x: x is a perfect square}
(vii) {x: x is perfect cube}
(viii) {x: x + 5 = 8}
(ix) {x: 2x + 5 = 9}
(x) {x: x ≥ 7}
(xi) {x: x ∈ N and 2x + 1 > 10}
Answer:
U = N: Set of natural numbers
(i) {x: x is an even natural number}´ = {x: x is an odd natural number}
(ii) {x: x is an odd natural number}´ = {x: x is an even natural number}
(iii) {x: x is a positive multiple of 3}´ = {x: x ∈ N and x is not a multiple of 3}
(iv) {x: x is a prime number}´ ={x: x is a positive composite number and x = 1}
(v) {x: x is a natural number divisible by 3 and 5}´ = {x: x is a natural number that is not divisible by 3 or 5}
(vi) {x: x is a perfect square}´ = {x: x ∈ N and x is not a perfect square}
(vii) {x: x is a perfect cube}´ = {x: x ∈ N and x is not a perfect cube}
(viii) {x: x + 5 = 8}´ = {x: x ∈ N and x ≠ 3}
(ix) {x: 2x + 5 = 9}´ = {x: x ∈ N and x ≠ 2}
(x) {x: x ≥ 7}´ = {x: x ∈ N and x < 7}
(xi) {x: x ∈ N and 2x + 1 > 10}´ = {x: x ∈ N and x ≤ 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) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3937/CHAPTER%201_html_m70c2b39f.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3937/CHAPTER%201_html_m14dcfbd2.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3937/CHAPTER%201_html_m70c2b39f.gif)
Answer:
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {2, 4, 6, 8}, B = {2, 3, 5, 7}
(i)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3937/CHAPTER%201_html_m677a9572.gif)
(ii)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3937/CHAPTER%201_html_m323d2141.gif)
Question 5:
Draw appropriate Venn diagram for each of the following:
(i) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3938/CHAPTER%201_html_dc5f1d8.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3938/CHAPTER%201_html_dc5f1d8.gif)
(ii) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3938/CHAPTER%201_html_m47e6a9ea.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3938/CHAPTER%201_html_m47e6a9ea.gif)
(iii) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3938/CHAPTER%201_html_1e95c54a.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3938/CHAPTER%201_html_1e95c54a.gif)
(iv) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3938/CHAPTER%201_html_m54b69d7c.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3938/CHAPTER%201_html_m54b69d7c.gif)
Answer:
(i) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3938/CHAPTER%201_html_dc5f1d8.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3938/CHAPTER%201_html_dc5f1d8.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3938/CHAPTER%201_html_m5a282086.jpg)
(ii) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3938/CHAPTER%201_html_m47e6a9ea.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3938/CHAPTER%201_html_m47e6a9ea.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3938/CHAPTER%201_html_m5a282086.jpg)
(iii) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3938/CHAPTER%201_html_1e95c54a.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3938/CHAPTER%201_html_1e95c54a.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3938/CHAPTER%201_html_29f1b55c.jpg)
(iv) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3938/CHAPTER%201_html_m54b69d7c.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3938/CHAPTER%201_html_m54b69d7c.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3938/CHAPTER%201_html_29f1b55c.jpg)
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
?
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3941/CHAPTER%201_html_m2c2c56cf.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3941/CHAPTER%201_html_m2c2c56cf.gif)
Page No 21:
Question 7:
Fill in the blanks to make each of the following a true statement:
(i) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3945/CHAPTER%201_html_62fa8558.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3945/CHAPTER%201_html_62fa8558.gif)
(ii) Φ′ ∩ A = …
(iii) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3945/CHAPTER%201_html_4431746f.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3945/CHAPTER%201_html_4431746f.gif)
(iv) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3945/CHAPTER%201_html_114ae2b3.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3945/CHAPTER%201_html_114ae2b3.gif)
Answer:
(i) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3945/CHAPTER%201_html_m7f6f1281.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/161/3945/CHAPTER%201_html_m7f6f1281.gif)
(ii) Φ′ ∩ A = U ∩ A = A
∴ Φ′ ∩ A = A
(iii) A ∩ A′ = Φ
(iv) U′ ∩ A = Φ ∩ A = Φ
∴ U′ ∩ A = Φ