Class 11 Maths Ncert Solutions Chapter 1 Ex 1.1 Sets PDF

# Class 11 Maths Ncert Solutions Ex 1.1

## Class 11 Maths Ncert Solutions Chapter 1 Ex 1.1

(a).  The collection of all day in a week which have the first letter S.

In a year we can easily identify all the days in a week which starts with the letter S. So it will form a clearly defined collection of objects.

Hence, the given collection can be a set.

(b).  The collection of ten most famous singers of India.

If we talk about the most famous singers then it is not a well-defined collection, because there are different parameters to be famous. So, it does not fall in this category.

Hence, the given collection cannot be a set.

(c).  A group of best football strikers of the world.

A group of best football strikers cannot be determined because each individual have different point of view to identify the best football strikers. So it does not form a well-defined collection.

Hence, this group is not a set.

(d).  The collection of all girls in your school.

The collection of all girls in your school can easily be identified as this category is clearly defined.

Hence, the given collection can be a set.

(e).  The collection of all odd numbers below 50.

The collection of all odd numbers below 50 can be identified by calculating, so it forms a well-defined collection. .

Hence, the given collection can be a set.

(f).  A collection of poems written by the poet Shakespeare.

A collection of all the poems written by Shakespeare can be identified easily as he has the copyright on all his poems. So it forms a well-defined collection.

Hence the given collection can be a set.

(g).  The collection of all prime numbers.

All prime numbers can be identified after doing some calculations and thus it forms a well-defined collection.

Hence, the given collection can be a set.

(h).  The collection of questions in science book.

We can find out the given question in a science book, so it will form a well-defined collection of objects.

Hence, the given collection can be a set.

(i).  A collection of most dangerous reptiles in India.

If we are talking about the most dangerous reptiles in India, and then it would be difficult to tell. This category will vary from person to person. So it does not fall in the category of well-defined collection.

Hence, the given collection cannot be a set.

Q.2: Let P = {2, 3, 4, 5, 6, 7}. Insert the correct symbol or$\in\:or\:\notin$ inside the given blank spaces below:

(a).  2 . . . . . . . . . . P

(b).  9 . . . . . . . . . P

(c).  11 . . . . . . . . P

(d).  4 . . . . . . . . P

(e).  0 . . . . . . . . P

(f).  7 . . . . . . . . P

(a).  2P$2\in\:P$

(b).  9P$9\notin\:P$

(c).  11P$11\notin\:P$

(d).  4P$4\in\:P$

(e).  0P$0\notin\:P$

(f).  7P$7\in\:P$

Q.3: Write the given sets in roster form:

(a).  P = {y: y is an integer and -4 < y < 6}.

(b).  Q = {y: y is a natural number which is <8}

(c).  R = {y: y is a 2 digit natural number in which the sum of its digits is 9}

(d).  S = {y: y is a prime number which is a divisor of 70}

(e).  T = The set of all letters in the word ELEPHANT

(f).  U = The set of all letters in the word DIVISION

(a).  P = {y: y is an integer and -4 < y < 6}

The elements from this given set are –3, –2,-1, 0, 1, 2, 3, 4, and 5 only.

Hence, we can write the following set in the roaster form as given below:

P = {–3, –2,-1, 0, 1, 2, 3, 4, 5}

(b).  Q = {y: y is a natural number which is <6}

The elements from this given set are 1, 2, 3, 4, 5, 6, and 7 only.

Hence, we can write the following set in the roaster form as given below:

Q = {1, 2, 3, 4, 5, 6, 7}

(c).  R = {y: y is a 2 digit natural number in which the sum of its digits is 9}

The elements from this given set are 18, 27, 36, 45, 54, 63, 72, 81 and 90 only.

Hence, we can write the following set in the roaster form as given below:

R = {18, 27, 36, 45, 54, 63, 72, 81, 90}

(d).  S = {y: y is a prime number which is a divisor of 140}

70 = 2 x 2 x 5 x 7

The elements from this given set are 2, 5, and 7 only.

Hence, we can write the following set in the roaster form as given below:

S = {2, 5, 7}.

(e).  T = The set of all letters in the word ELEPHANT

There are 8 letters in the given word ELEPHANT, out of which L is repeated.

Hence, we can write the following set in the roaster form as given below:

T = {E, L, P, H, A, N, T}

(f).  U = The set of all letters in the word DIVISION

There are 8 letters in the given word DIVISION, out of which I is repeated.

Hence, we can write the following set in the roaster form as given below:

U = {D, I, V, S, O, N}

Q.4: Write the given sets in set-builder form:

(a).  {4, 8, 12, 16, 20}

(b).  {3, 9, 27, 81}

(c).  {4, 16, 64, 256, 1024}

(d).  {1, 3, 5, 7…}

(e).  {1, 8, 27, 64….1000}

(a). {4, 8, 12, 16, 20} = {y: y = 4n, nPand1n5$n\in\:P\:and\:1\leq n\leq 5$}

(b).  {3, 9, 27, 81}

We can see here that 3=31$3=3^{1}$, 9=32$9=3^{2}$, 27=33$27=3^{3}$, 81=34$81=3^{4}$.

Hence, {3, 9, 27, 81} = {y: y = 3n, nPand1n4$n\in\:P\:and\:1\leq n\leq 4$

(c).  {4, 16, 64, 256, 1024}

We can see here that 4=41,16=42,64=43,256=44,1024=45$4=4^{1},16=4^{2},64=4^{3},256=4^{4},1024=4^{5}$

Hence, {4, 16, 64, 256, 1024} = {y: y = 4n, nPand1n5$n\in\:P\:and\:1\leq n\leq 5$

(d).  {1, 3, 5, 7…}

Above mentioned that the numbers are the set of odd natural numbers.

Hence, {1, 3, 5, 7…} = {y: y is an odd natural numbers}

(e).  {1, 8, 27, 64….1000}

We can see here that 1=13,2=23,3=33,4=43,1000=103$1=1^{3},2=2^{3},3=3^{3},4=4^{3},…1000=10^{3}$

Hence, {1, 8, 27, 64….1000} = {y: y = n2, nPand1n10$n\in\:P\:and\:1\leq n\leq 10$

Q.5: List all the elements from the given sets:

(a).  P = {y: y is even natural number}

(b).  Q = {y: y is an integer, 12<y<92$\frac{-1}{2}< y< \frac{9}{2}$}

(c).  R = {y: y is an integer; y24$y^{2}\leq 4$}

(d).  S = {y: y is letter in the word “TIFFIN”}

(e).  T = {y: y is a month of a year having 31 days}

(f).  U = {y: y is a consonant in the English alphabet which precedes m}

(a).  P = {y: y is even natural number} = {2, 4, 6, 8, 10 …..}

(b).  Q = {y: y is an integer, 12<y<92$\frac{-1}{2}< y< \frac{9}{2}$}

We can see that 12=0.5and92=4.5$\frac{-1}{2}=0.5\:and\:\frac{9}{2}=4.5$

Hence, Q = {0, 1, 2, 3, 4}

(c).  R = {y: y is an integer; y24$y^{2}\leq 4$}

We can see that (1)2=14;(2)2=44;(3)2=9>4$\left ( -1 \right )^{2}=1\leq 4;\left ( -2 \right )^{2}=4\leq 4;\left ( -3 \right )^{2}=9> 4$

$\Rightarrow$   02=04$0^{2}=0\leq 4$

$\Rightarrow$   12=14$1^{2}=1\leq 4$

$\Rightarrow$   22=44$2^{2}=4\leq 4$

$\Rightarrow$  32=9>4$3^{2}=9> 4$

Hence, R = {-2, -1, 0, 1, 2}

(d).  S = {y: y is letter in the word “TIFFIN”}

= {T, I, F, N}

(e).  T = {y: y is a month of a year having 31 days}

= {January, March, May, July, September, November}

(f).  U = {y: y is a non-vowel alphabet in English which comes before m}

= {b, c, d, f, g, h, j, k, l}

Q.6: Match the following:

 (A) {1, 2, 3, 6} (i) {y: y is a divisor of 6 and also a prime number} (B) {T, R, I, G, O, N, M, E, Y} (ii) {y: y is less than 10 and also an odd number} (C) {2, 3} (iii) {y: y is natural number divisor of 6} (D) {1, 3, 5, 7, 9} (iv) {y: y is a letter of the word TRIGONOMETRY}