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**Exercise 1.3**

**1. Make correct statements by filling in the symbols **** or **** in the blank spaces:**

**(i) {2, 3, 4} _______ {1, 2, 3, 4, 5}**

**(ii) **

**(iii) {**** is a student of class XI of your school} _______ {**** student of your school}**

**(iv) {**** is a circle in the plane} _______ {**** is a circle in the same plane with 1 unit}**

**(v) {**** is a triangle in plane} _______ {****is a rectangle in the same plane}**

**(vi) {**** is an equilateral triangle in a plane} _______ {**** is a rectangle in the same plane}**

**(vii) {**** is an even natural number} _______ {**** is an integer}**

**Ans.** **(i)**

**(ii)**

**(iii)**

**(iv)**

**(v)**

**(vi)**

**(vii)**

**2. Examine whether the following statements are true or false:**

**(i) **

**(ii) **** {**** is a vowel in the English alphabet}**

**(iii) **

**(iv) **

**(v) **

**(vi) {**** is an even natural number less than 6}****{**** is a natural number which divide 36}**

**Ans. (i) **Let A = and B =

Here, every element of set A is an element of set B.

A B

Therefore, statement is false.

**(ii) **Let A = and B

= { is a vowel in the English alphabet}

=

Here, every element of set A is an element of set B.

A B

Therefore, statement is true.

**(iii) **Let A = {1, 2, 3} and B = {1, 3, 5}

Here, 2 A but 2 B

A B

Therefore, statement is false.

**(iv) **Let A = and B =

Here, every element of set A is an element of set B.

A B

Therefore, statement is true.

**(v) **Let A = and B =

Here, B

Therefore, statement is false.

**(vi) **Let A = { is an even natural number less than 6}

= {2, 4}

And B = }{ is a natural number which divide 36}

= {1, 2, 3, 4, 6, 12, 18, 36]

Here, every element of set A is an element of set B.

A B

Therefore, statement is true.

**3. Let A = {1, 2, {3, 4}, 5}. Which of the following statements are incorrect and why:**

**(i) {3, 4} A **

**(ii) {3, 4} A **

**(iii) {{3, 4}} A**

**(iv) 1 A **

**(v) 1 A **

**(vi) {1, 2, 5} A**

**(vii) {1, 2, 5} A **

**(viii) {1, 2, 3} A **

**(ix) A**

**(x) A**

**Ans. (i) **{3, 4} is a member of set A.

{3, 4} A

Therefore, {3, 4} A is incorrect.

**(ii) **{3, 4} is a member of set A. Therefore, {3, 4} A is incorrect.

**(iii) **{3, 4} is a member of set A.

{{3, 4}} is a set.

Therefore, {{3, 4}} A is incorrect

**(iv) **1 is a member of set A. Therefore 1 A is correct.

**(v) **1 is not a set, it is a member of set A. Therefore, 1 A is incorrect.

**(vi) **1, 2, 5 are the members of set A.

{1, 2, 5} is a subset of set A.

Therefore, {1, 2, 5} A is correct.

**(vii) **1, 2, 5 are the members of set A.

{1, 2, 5} is a subset of set A.

Therefore, {1, 2, 5} A is incorrect.

**(viii) **3 is not a member of set A.

{1, 2, 3} is not a subset of set A.

Therefore, {1, 2, 3} A is incorrect.

**(ix) ** is not a member of set A. Therefore, A is correct.

**(x) ** is not a member of set A. Therefore, A is incorrect.

**4. Write down all the subsets of the following sets:**

**(i) **

**(ii) **

**(iii) {1, 2, 3} **

**(iv) **

**Ans. (i) **Number of elements in given set = 1.

Number of subsets of given set = = 2

Therefore, Subsets of given set are

**(ii) **Number of elements in given set = 2

Number of subsets of given set = = 4

Therefore, Subsets of given set are

**(iii) **Number of elements in given set = 3

Number of subsets of given set = = 8

Therefore, Subsets of given set are

**(iv) **Number of elements in given set = 0

Number of subsets of given set = = 1

Therefore, Subsets of given set are

**5. How many elements has P(A), if A = **** ?**

**Ans. **Number of elements in set A = 0

Number of subsets of given set = = 1

Therefore, number of elements of P (A) is 1.

**6. Write the following as intervals:**

**(i) { R, } **

**(ii) { R, }**

**(iii) { R, } **

**(iv) { R, }**

**Ans. (i) **Let A = { R, }

It can be written in the form of interval as

**(ii) **Let A = { R, }

It can be written in the form of interval as

**(iii) **Let A = { R, }

It can be written in the form of interval as

**(iv) **Let A = { R, }

It can be written in the form of interval as

**7. Write the following intervals in set-builder form:**

**(i) **

**(ii) [6, 12] **

**(iii) (6, 12] **

**(iv) **

**Ans. (i)** { R, }

**(ii)** { R, }

**(iii)** { R, }

**(iv)** { R, }

**8. What universal set(s) would you propose for each of the following:**

**(i) The set of right triangles **

**(ii) The set of isosceles triangles**

**Ans. (i) **Right triangle is a type of triangle. Therefore, the set of triangles contain all types of triangles.

U = { is a triangle in plane}

**(ii) **Isosceles triangle is a type of triangle. Therefore, the set of triangles contain all types of triangles.

U = { is a triangle in plane}

**9. Given the set A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set(s) for all the three sets A, B and C:**

**(i) {0, 1, 2, 3, 4, 5, 6} **

**(ii) **

**(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} **

**(iv) {1, 2, 3, 4, 5, 6, 7, 8}**

**Ans. (i) **{0, 1, 2, 3, 4, 5, 6} is not a universal set for A, B, C because 8 C but 8 is not a member of {0, 1, 2, 3, 4, 5, 6}.

**(ii) ** is a set which contains no element. therefore, it is not a universal set for A, B, C.

**(iii) **{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is a universal set for A, B, C because all members of A, B, C are present in {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

**(iv) **{1, 2, 3, 4, 5, 6, 7, 8} is not a universal set for A, B, C because 0 C but 0 is not a member of {1, 2, 3, 4, 5, 6, 7, 8}.

Ap apna first sum ka 4th part dekho galat hai??

Q2 no.6 Does 4 divide 36 ? I don’t think it does. So the answer will be false.

Sorry. The answer is correct.

?????

Nicely way to help student thank you so much