NCERT Answers for Class 11 Math's Section 1 - Sets Exercise 1.1,1.2

 Practice 1.1

1. Which of the following are sets? Legitimize your response.

(I) The assortment of the entire months of a year starting with the letter J.

(ii) The assortment of ten most capable journalists of India.

(iii) A group of eleven best-cricket batsmen of the world.

(iv) The assortment of all young men in your group.

(v) The assortment of all regular numbers under 100.

(vi) An assortment of books composed by the essayist Munshi Prem Chand.

(vii) The assortment of every even number.

(viii) The assortment of inquiries in this Section.

(ix) An assortment of the most perilous creatures of the world.

Solution:

(I) The assortment of the entire months of a year starting with the letter J is a distinct assortment of items as one can recognize a month which has a place with this assortment.

Thus, this assortment is a set.

(ii) The assortment of ten most gifted scholars of India is certainly not an obvious assortment as the models to decide an essayist's ability might contrast starting with one individual then onto the next.

Subsequently, this assortment is certainly not a set.

(iii) A group of eleven best-cricket batsmen of the world is certainly not a distinct assortment as the measures to decide a batsman's ability might differ starting with one individual then onto the next.

Hence, this assortment is definitely not a set.

(iv) The assortment of all young men in your group is a clear-cut assortment as you can distinguish a kid who has a place with this assortment.

Consequently, this assortment is a set.

(v) The assortment of all regular numbers under 100 is an obvious assortment as one can find a number which has a place with this assortment.

Consequently, this assortment is a set.

(vi) An assortment of books composed by the essayist Munshi Prem Chand is a distinct assortment as one can find any book which has a place with this assortment.

Subsequently, this assortment is a set.

(vii) The assortment of all even whole numbers is a clear-cut assortment as one can find a number which has a place with this assortment.

Subsequently, this assortment is a set.

(viii) The assortment of inquiries in this section is a distinct assortment as one can find an inquiry which has a place with this part.

Subsequently, this assortment is a set.

(ix) An assortment of most perilous creatures of the world is definitely not an obvious assortment as the models to find the hazardousness of a creature can contrast starting with one creature then onto the next.

2. Compose the accompanying sets in program structure:

(I) A = {x: x is a number and - 3 < x < 7}.

(ii) B = {x: x is a characteristic number under 6}.

(iii) C = {x: x is a two-digit normal number with the end goal that the amount of its digits is 8}

(iv) D = {x: x is an indivisible number which is divisor of 60}.

(v) E = The arrangement of all letters in the word Geometry.

(vi) F = The arrangement of all letters in the word BETTER.

Solution:

(I) A = {x: x is a whole number and - 3 < x < 7}

-2, - 1, 0, 1, 2, 3, 4, 5, and 6 just are the components of this set.

Subsequently, the given set can be written in program structure as

A = {-2, - 1, 0, 1, 2, 3, 4, 5, 6}

(ii) B = {x: x is a characteristic number under 6}

1, 2, 3, 4, and 5 just are the components of this set

Consequently, the given set can be written in program structure as

B = {1, 2, 3, 4, 5}

(iii) C = {x: x is a two-digit regular number to such an extent that the amount of its digits is 8}

17, 26, 35, 44, 53, 62, 71, and 80 just are the components of this set

Thus, the given set can be written in list structure as

C = {17, 26, 35, 44, 53, 62, 71, 80}

(iv) D = {x: x is an indivisible number which is divisor of 60}

NCERT Arrangements Class 11 Section 1 Ex 1.1 Picture 1

Here 60 = 2 × 2 × 3 × 5

2, 3 and 5 just are the components of this set

Consequently, the given set can be written in program structure as

D = {2, 3, 5}

(v) E = The arrangement of all letters in the word Geometry

Geometry is a 12 letters word out of which T, R and O are rehashed.

Subsequently, the given set can be written in list structure as

E = {T, R, I, G, O, N, M, E, Y}

(vi) F = The arrangement of all letters in the word BETTER

BETTER is a 6 letters word out of which E and T are rehashed.

Subsequently, the given set can be written in list structure as

F = {B, E, T, R}

3. List every one of the components of the accompanying sets:

(I) A = {x: x is an odd normal number}

(ii) B = {x: x is a whole number, - 1/2 < x < 9/2}

(iii) C = {x: x is a whole number, x2 ≤ 4}

(iv) D = {x: x is a letter in "LOYAL"}

(v) E = {x: x is a month of a year not having 31 days}

(vi) F = {x: x is a consonant in the English letter set which continues k}.

Solution:

(I) A = {x: x is an odd normal number}

So, the components are A = {1, 3, 5, 7, 9 ….}

(ii) B = {x: x is a number, - 1/2 < x < 9/2}

That's what we know - 1/2 = - 0.5 and 9/2 = 4.5

So, the components are B = {0, 1, 2, 3, 4}.

(iii) C = {x: x is a whole number, x2 ≤ 4}

That's what we know.

(-1)2 = 1 ≤ 4; (- 2)2 = 4 ≤ 4; (- 3)2 = 9 > 4

Here

02 = 0 ≤ 4, 12 = 1 ≤ 4, 22 = 4 ≤ 4, 32 = 9 > 4

So, we get.

C = {-2, - 1, 0, 1, 2}

(iv) D = {x: x is a letter in "LOYAL"}

So, the components are D = {L, O, Y, A}

(v) E = {x: x is a month of a year not having 31 days}

So, the components are E = {February, April, June, September, November}

(vi) F = {x: x is a consonant in the English letters in order which continues k}

So, the components are F = {b, c, d, f, g, h, j}

4. Let A = {1, 2, 3, 4, 5, 6}. Embed the suitable image ∈or ∉ in the clear spaces:

(I) 5… A

(ii) 8… A

(iii) 0… A

(iv) 4… A

(v) 2… A

(vi) 10… A

Solution:

(I) 5 ∈ A

(ii) 8 ∉ A

(iii) 0 ∉ A

(iv) 4 ∈ A

(v) 2 ∈ A

(vi) 10 ∉ A

5. Compose the accompanying sets in the set-developer structure:

(I) (3, 6, 9, 12)

(ii) {2, 4, 8, 16, 32}

(iii) {5, 25, 125, 625}

(iv) {2, 4, 6 …}

(v) {1, 4, 9 … 100}

Solution:

(I) {3, 6, 9, 12}

The given set can be written in the set-developer structure as {x: x = 3n, n ∈ N and 1 ≤ n ≤ 4}

(ii) {2, 4, 8, 16, 32}

We know that 2 = 21, 4 = 22, 8 = 23, 16 = 24, and 32 = 25.

Accordingly, the given set {2, 4, 8, 16, 32} can be written in the set-developer structure as {x: x = 2n, n ∈ N and 1 ≤ n ≤ 5}.

(iii) {5, 25, 125, 625}

We know that 5 = 51, 25 = 52, 125 = 53, and 625 = 54.

In this way, the given set {5, 25, 125, 625} can be written in the set-developer structure as {x: x = 5n, n ∈N and 1 ≤ n ≤ 4}.

(iv) {2, 4, 6 …}

{2, 4, 6 …} is a bunch of all even regular numbers.

Consequently, the given set {2, 4, 6 …} can be written in the set-developer structure as {x: x is an even regular number}.

(v) {1, 4, 9 … 100}

We know that 1 = 12, 4 = 22, 9 = 32 … 100 = 102.

Accordingly, the given set {1, 4, 9… 100} can be written in the set-developer structure as {x: x = n2, n ∈ N and 1 ≤ n ≤ 10}.

6.Match every one of the sets on the left in the program structure with a similar set on the right portrayed in set-developer structure:

(I) {1, 2, 3, 6} (a) {x: x is an indivisible number and a divisor of 6}

(ii) {2, 3} (b) {x: x is an odd regular number under 10}

(iii) {M, A, T, H, E, I, C, S} (c) {x: x is a characteristic number and divisor of 6}

(iv) {1, 3, 5, 7, 9} (d) {x: x is a letter of the word MATHEMATICS}

Solution:

(I) Here the components of this set are normal numbers as well as divisors of 6. Thus, (I) coordinates with (c).

(ii) 2 and 3 are indivisible numbers which are divisors of 6. Subsequently, (ii) coordinates with (a).

(iii) The components are the letters of the word Science. Subsequently, (iii) coordinates with (d).

(iv) The components are odd normal numbers which are under 10. Consequently, (v) coordinates with (b).

Practice 1.2

1. Which of the following are instances of the invalid set?

(I) Set of odd normal numbers distinct by 2

(ii) Set of even indivisible numbers

(iii) {x: x is a characteristic number, x < 5 and x > 7}

(iv) {y: y is a guide normal toward any two equal lines}

Solution:

(I) Set of odd normal numbers distinguishable by 2 is an invalid set as odd numbers are not separable by 2.

(ii) Set of even indivisible numbers is definitely not an invalid set as 2 is an even indivisible number.

(iii) {x: x is a characteristic number, x < 5 and x > 7} is an invalid set as a number can't be both under 5 and more prominent than 7.

(iv) {y: y is a direct normal toward any two equal lines} is an invalid set as the equal lines don't cross. Hence, they have no normal point.

2. State whether every one of the accompanying sets is limited or endless:

(I) The arrangement of lines which are lined up with the x-hub

(ii) The arrangement of letters in the English letter set

(iii) The arrangement of numbers which are different of 5

(iv) The arrangement of creatures living on the earth

(v) The arrangement of circles going through the beginning (0, 0)

Solution:

(I) The arrangement of lines which are lined up with the x-pivot is a boundless set as the lines which are lined up with the x-hub are limitless.

(ii) The arrangement of letters in the English letters in order is a limited set as it contains 26 components.

(iii) The arrangement of numbers which are various of 5 is a limitless set as the products of 5 are endless.

(iv) The arrangement of creatures living on the earth is a limited set as the quantity of creatures living on the earth is limited.

(v) The arrangement of circles going through the beginning (0, 0) is a boundless set as a limitless number of circles can go through the beginning.

3. Are the accompanying sets equivalent? Give reasons.

(I) A = {2, 3}; B = {x: x is arrangement of x2 + 5x + 6 = 0}

(ii) A = {x: x is a letter in the word FOLLOW}; B = {y: y is a letter in the word WOLF}

Arrangement:

(I) A = {2, 3}; B = {x: x is arrangement of x2 + 5x + 6 = 0}

x2 + 5x + 6 = 0 can be composed as

x (x + 3) + 2(x + 3) = 0

By additional estimation

(x + 2) (x + 3) = 0

So, we get.

x = - 2 or x = - 3

Here

A = {2, 3}; B = {-2, - 3}

In this way, A ≠ B

(ii) A = {x: x is a letter in the word FOLLOW} = {F, O, L, W}

B = {y: y is a letter in the word WOLF} = {W, O, L, F}

Requests in which the components of a set which are recorded aren't huge.

Hence, A = B.

4. Which of the accompanying sets are limited or boundless?

(I) The arrangement of months of a year

(ii) {1, 2, 3 …}

(iii) {1, 2, 3 … 99, 100}

(iv) The arrangement of positive whole numbers more prominent than 100

(v) The arrangement of indivisible numbers under 99

Solution:

(I) The arrangement of months of a year is a limited set as it contains 12 components.

(ii) {1, 2, 3 …} is a limitless set since it has a boundless number of regular numbers.

(iii) {1, 2, 3 … 99, 100} is a limited set as the numbers from 1 to 100 are limited.

(iv) The arrangement of positive whole numbers more noteworthy than 100 is a limitless set as the positive numbers which are more noteworthy than 100 are endless.

(v) The arrangement of indivisible numbers under 99 is a limited set as the indivisible numbers which are under 99 are limited.

5.In the accompanying, state regardless of whether A = B:

(I) A = {a, b, c, d}; B = {d, c, b, a}

(ii) A = {4, 8, 12, 16}; B = {8, 4, 16, 18}

(iii) A = {2, 4, 6, 8, 10}; B = {x: x is positive even whole number and x ≤ 10}

(iv) A = {x: x is a numerous of 10}; B = {10, 15, 20, 25, 30 …}

Solution:

(I) A = {a, b, c, d}; B = {d, c, b, a}

Requests in which the components of a set are recorded isn't huge.

Consequently, A = B.

(ii) A = {4, 8, 12, 16}; B = {8, 4, 16, 18}

We know that 12 ∈ A yet 12 ∉ B.

In this way, A ≠ B

(iii) A = {2, 4, 6, 8, 10}.

B = {x: x is a positive even whole number and x ≤ 10} = {2, 4, 6, 8, 10}

In this manner, A = B

(iv) A = {x: x is a various of 10}

B = {10, 15, 20, 25, 30 …}

We know that 15 ∈ B yet 15 ∉ A.

In this manner, A ≠ B

6. From the sets given underneath, select equivalent sets:

A = {2, 4, 8, 12}, B = {1, 2, 3, 4}, C = {4, 8, 12, 14}, D = {3, 1, 4, 2}

E = {-1, 1}, F = {0, a}, G = {1, - 1}, H = {0, 1}

Solution:

A = {2, 4, 8, 12}; B = {1, 2, 3, 4}; C = {4, 8, 12, 14}

D = {3, 1, 4, 2}; E = {-1, 1}; F = {0, a}

G = {1, - 1}; H = {0, 1}

That's what we know.

8 ∈ A, 8 ∉ B, 8 ∉ D, 8 ∉ E, 8 ∉ F, 8 ∉ G, 8 ∉ H

A ≠ B, A ≠ D, A ≠ E, A ≠ F, A ≠ G, A ≠ H

It tends to be composed as

2 ∈ A, 2 ∉ C

In this manner, A ≠ C

3 ∈ B, 3 ∉ C, 3 ∉ E, 3 ∉ F, 3 ∉ G, 3 ∉ H

B ≠ C, B ≠ E, B ≠ F, B ≠ G, B ≠ H

It tends to be composed as

12 ∈ C, 12 ∉ D, 12 ∉ E, 12 ∉ F, 12 ∉ G, 12 ∉ H

Accordingly, C ≠ D, C ≠ E, C ≠ F, C ≠ G, C ≠ H

4 ∈ D, 4 ∉ E, 4 ∉ F, 4 ∉ G, 4 ∉ H

Accordingly, D ≠ E, D ≠ F, D ≠ G, D ≠ H

Here, E ≠ F, E ≠ G, E ≠ H

F ≠ G, F ≠ H, G ≠ H

Requests in which the components of a set are recorded isn't huge.

B = D and E = G

Accordingly, among the given sets, B = D and E = G.