NCERT Solutions class-11 Maths Exercise 1.3

Exercise 1.3

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

(ii)

(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)

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

(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.

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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.

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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

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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.

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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

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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, }

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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}

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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}.