NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.2
Ex 1.2 Class 11 Maths Question 1.
Which of the following are examples of the null set?(i) Set of odd natural numbers divisible by 2
(ii) Set of even prime numbers
(iii) {x: x is a natural number, x < 5 and x > 7}
(iv) {y: y is a point common to any two parallel lines}
Solution.
(i) The set of odd natural numbers divisible by 2 is a null set
because odd natural numbers are not divisible by 2.
(ii) The set of even prime numbers is {2} which is not a null set.
(iii) {x: x is a natural number, x < 5 and x >7} is a null
set because there is no natural number which satisfies x < 5 and x > 7
simultaneously.
(iv) {y: y is a point common to any two parallel lines} is a null
set because two parallel lines do not have any common point.
Ex 1.2 Class 11 Maths Question 2.
Which of the following sets are finite or infinite?(i) The set of months of a year
(ii) {1, 2, 3, …}
(iii) {1, 2, 3, …, 99, 100}
(iv) The set of positive integers greater than 100
(v) The set of prime numbers less than 99
Solution.
(i) The
set of months of a year is finite set because there are 12 months in a year.
(ii) {1,
2, 3, …} is an infinite set because there are infinite number of elements in
the set.
(iii) {1,
2, 3, …, 99, 100) is a finite set because the set contains finite number of
elements.
(iv) The
set of positive integers greater than 100 is an infinite set because there are
infinite number of positive integers greater than 100.
(v) The
set of prime numbers less than 99 is a finite set because the set contains
finite number of elements.
Ex 1.2 Class 11 Maths Question 3.
State whether each of the following set is finite or infinite:(i) The set of lines which are parallel to the x-axis
(ii) The set of letters in the English alphabet
(iii) The set of numbers which are multiple of 5
(iv) The set of animals living on the earth
(v) The set of circles passing through the origin (0, 0)
Solution.
(i) The
set of lines which are parallel to the x-axis is an infinite set because we can
draw infinite number of lines parallel to x-axis.
(ii) The
set of letters in the English alphabet is a finite set because there are 26
letters in the English alphabet.
(iii) The
set of numbers which are multiple of 5 is an infinite set because there are
infinite number of multiples of 5, i.e., 5, 10, 15, 20, …….
(iv) The
set of animals living on the earth is a finite set because the number of
animals living on the earth is very large but finite.
(v) The
set of circles passing through the origin (0, 0) is an infinite set because we
can draw infinite number of circles passing through origin with different
radii.
Ex 1.2 Class 11 Maths Question 4.
In the following, state whether A = B or not:(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 integer and x ≤ 10}
(iv) A = {x: x is a multiple of 10}; B = {10, 15, 20, 25, 30, …}
Solution.
(i) A
= {a, b, c, d} and B = {d, c, b, a} are equal sets because order of elements
does not change a set.
∴ A = B = {a, b, c, d}
(ii) A = {4, 8, 12, 16} and B = {8, 4,
16, 18} are not equal sets because 12 ∈ A but 12 ∉ B and 18 ∈ B but 18 ∉ A.
(iii) A = {2, 4, 6, 8, 10} and B = {x: x
is a positive even integer and x ≤ 10) which can be written in roster form as B
= (2, 4, 6, 8, 10) are equal sets.
∴ A = B = {2, 4, 6, 8, 10}
(iv) A = {x: x is a multiple of 10) can
be written in roster form as A = {10, 20, 30, 40, ……..} and B = {10, 15, 20,
25, 30, ………..} are not equal sets because 15 ∈ B but 15 ∉ A.
Ex 1.2 Class 11 Maths Question 5.
Are the following pairs of sets equal? Give reasons.(i) A = {2, 3}; B = {x: x is solution 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}
Solution.
(i) A
= (2, 3} and B = {x: x is a solution of x2 + 5x + 6 = 0}
Now, x2 + 5x + 6 = 0 ⇒ x2 + 3x + 2x + 6 = 0
⇒ (x + 3)(x + 2) = 0
⇒ x = -3, -2
∴ B = {-2, -3}
Hence, A and B are not equal sets.
(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}
Hence, A = B = {F, O, L, W}
Ex 1.2 Class 11 Maths Question 6
From the sets given below, select equal 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.
From the given sets, we see that sets B and D have the same elements and also
sets E and G have the same elements.
∴ B = D = {1 ,2, 3, 4} and E = G = {-1,
1}.
Related Links:
NCERT Solutions for Maths Class 9