EXERCISE 1.2
1. Which of the following are examples of the null set? (Ex 1.2 sets ncert maths solution class 11)
(i) Set of odd natural numbers divisible by 2
(ii) Set of even prime numbers
(iii) {x: x is a natural numbers, x < 5 and x > 7}
(iv) {y: y is a point common to any two parallel lines}
Solution: (i) Set of odd natural numbers is a null set, as odd numbers are not divisible by 2.
(ii) Set of even prime numbers is not a null set, as 2 is an even prime number.
(iii) {x: x is a natural number, 
and 
} is a null set, a number cannot be both less than 5 and greater than 7.
(iv) {y: y is a point common to any two parallel lines} is a null set, the parallel lines do not intersect. Therefore, they have no common point.
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 a finite set, as it contains 12 elements.
(ii) 
is an infinite set because it has an infinite number of natural numbers.
(iii) 
is a finite set.
(iv) The set of positive integers greater than 100 is an infinite set,
(v) The set of prime numbers less than 99 is a finite set.
3. State whether each of the following sets 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.
(ii) The set of letters in the English alphabet is a finite set, it contains 26 elements.
(iii) The set of numbers which are multiple of 5 is an infinite set.
(iv) The set of animals living on the earth is a finite set, the number of animals living on the earth is finite.
(v) The set of circles passing through the origin (0, 0) is an infinite set.
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}; B = {d, c, b, a}
The order in which the elements of a set are listed is not significant.
Therefore, 
.
(ii) A = {4, 8, 12, 16}; B = {8, 4, 16, 18}
We know that 12 ∈ A but 12 ∉ B.
Therefore, 
(iii) A = {2, 4, 6, 8, 10};
B = {x: x is a positive even integer and x ≤ 10} = {2, 4, 6, 8, 10}
Therefore,
(iv) A = {x: x is a multiple of 10}
B = {10, 15, 20, 25, 30 …}
We know that 15 ∈ B but 15 ∉ A.
Therefore,
5. Are the following pair 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}; B = {x: x is solution of x2 + 5x + 6 = 0}
x2 + 5x + 6 = 0 can be written as
⇒ x(x + 3) + 2(x + 3) = 0
⇒ (x + 2) (x + 3) = 0
So, we get
x = –2 or x = –3
Here,
A = {2, 3}; B = {–2, –3}
Therefore,
(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}
The order in which the elements of a set which are listed is not significant.
Therefore, .
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: 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}
From above sets
B = D and E = G
Therefore, among the given sets, B = D and E = G.
