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# Class 11 NCERT Solutions – Chapter 1 Sets – Exercise 1.5

• Difficulty Level : Hard
• Last Updated : 21 Jun, 2022

### (a) A’

Solution:

We know that this is the complement of set A i.e, it is the subset of U.

So, A’ = {5, 6, 7, 8, 9}

### (b) B’

Solution:

We know that this is the complement of set B i.e, it is the subset of U.

So, B’ = {1, 3, 5, 7, 9}

### (c) (A âˆª C)’

Solution:

This is the complement of union of set A and set C i.e, U – (Aâˆª C)

So, Aâˆª C = {1, 2, 3, 4, 5, 6}

=> U – (A âˆª C)

So, (Aâˆª C)’ = {7, 8, 9}

### (d) (A âˆª B)’

Solution:

This is complement of union of set A and set B i.e, U- (AâˆªB)

So, Aâˆª B = {1, 2, 3, 4, 6, 8}

=> U – (A âˆª B)

So, (A âˆª B)’ = {5, 7, 9}

### (e) (A’)’

Solution:

This is the complement of set A i.e, (A’)’ = A

So, (A’)’ = {1, 2, 3, 4}

### (f) (B – C)’

Solution:

(B – C) = elements in B but not in C

(B – C) = {2, 8}

=> U – (B – C)

So, (B – C)’ = {1, 3, 4, 5, 6, 7, 9}

### (a) A = {a, b, c}

Solution:

Complement of set A = A’

A’ = U – A

A’ = {a, b, c, d, e, f, g, h} – {a, b, c}

A’ = {d, e, f, g, h}

### (b) B = {d, e, f, g}

Solution:

Complement of set B = B’

B’ = U – B

B’ = {a, b, c, d, e, f, g, h} – {d, e, f, g}

B’ = {a, b, c, h}

### (c) C = {a, c, e, g}

Solution:

Complement of set C = C’

C’ = U – C

C’ = {a, b, c, d, e, f, g, h} – {a, c, e, g}

C’ = {b, d, f, h}

### (d) D = {f, g, h, a}

Solution:

Complement of set D = D’

D’ = U – D

D’ = {a, b, c, d, e, f, g, h} – {f, g, h, a}

D’ = {b, c, d, e}

### Question 3. Taking the set of natural numbers as the universal set, write down the complements of the following sets:

U = N: set of natural numbers

(a) {x : x is an even natural number}

=> {x : x is an odd natural number}

(b) {x : x is an odd natural number}

=>{x : x is an even natural number}

(c) {x : x is a positive multiple of 3}

=>{x : xâˆˆN and x is not a multiple of 3}

(d) {x : x is a prime number}

=> {x : x is a positive composite number and x=1}

(e) {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}

(f) {x : x is a perfect square}

=> {x : xâˆˆN and x is not perfect square}

(g) {x : x is a perfect cube}

=> {x : xâˆˆN and x is not perfect cube}

(h) {x : x + 5 = 8}

=> {x : xâˆˆN  and xâ‰ 3}

(i) {x : 2x + 5 = 9}

=> {x : xâˆˆN  and xâ‰ 2}

(j) {x : x â‰¥ 7}

=> {x : xâˆˆN  and x<7}

(k) {x : x âˆˆ N and 2x + 1 > 10}

=> {x : xâˆˆN and xâ‰¤ 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

(a) (A âˆª B)’= A’ âˆ© B’

Solution:

=> (A âˆª B)’= U – (AâˆªB)

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

=> (AâˆªB)’ = {1, 9}

=> {1, 3, 5, 7, 9} âˆ© {1, 4, 6, 8, 9}

=> A’ âˆ© B’ = {1, 9}

Hence, Verified!!!  (Aâˆª B)’ = A’ âˆ© B’

(b) (A âˆ© B)â€² = Aâ€² âˆª Bâ€²

=> {1, 2, 3, 4, 5, 6, 7, 8, 9} – {2}

=> (A âˆ© B)â€² = {1, 3, 4, 5, 6, 7, 8, 9}

A’ âˆª B’= (U – A) âˆª (U – B)

=> {1, 3, 5, 7, 9} âˆª {1, 4, 6, 8, 9}

=> Aâ€² âˆª Bâ€² = {1, 3, 4, 5, 6, 7, 8, 9}

Hence, Verified!!!  (A âˆ© B)â€² = Aâ€² âˆª Bâ€²

### Question 5. Draw appropriate Venn diagram for each of the following:

(a) (A âˆª B)â€²=

(d) Aâ€² âˆª Bâ€²

### Question 6. Let U be the set of all triangles in a plane. If A is the set of all triangles with atleast one angle different from 60Â°, what is Aâ€²?

Solution:

U = set of all triangles in plane

A = set of all triangles with at least one angle different from 60Â°

A’ = set of all triangles with no angle different from 60Â° i.e, set of all triangles with all angles 60Â°

A’ is the set of all equilateral triangle.

### Question 7. Fill in the blanks to make each of the following a true statement :

Solution:

(a) A âˆª Aâ€² = U

(b) âˆ…â€² âˆ© A = A

(c) A âˆ© Aâ€² = âˆ…