Practicing the AP Board Solutions Class 11 Maths and Chapter 1 Inter 1st Year Maths Sets Solutions Exercise 1b Pdf Download will help students to clear their doubts quickly.
Intermediate 1st Year Maths Sets Solutions Exercise 1b
Sets Exercise 1b Solutions
Sets Class 11 Exercise 1b Solutions – Sets 1b Exercise Solutions
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 null, as odd numbers are not divisible by 2.
(ii) The set of even prime numbers is not null, as 2 is an even Prime Number.
(iii) { x: x is a natural number, x < 5 and x > 7} is a null set as a number cannot be both than 5 and greater than 7.
(iv) {y: y is a point common to any two parallel lines} is a null set as the parallel lines do not intersect.
Therefore, they have no common point.
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 as it contains 12 elements.
(ii) {1, 2, 3,…} is an infinite set because it has an infinite number of natural numbers.
(iii) {1, 2, 3,…, 99, 100} is a finite set, as the numbers from 1 to 100 are finite.
(iv) The set of positive integers greater than 100 is infinite as the positive integers that are greater than 100 are infinite.
(v) The set of prime numbers less than 99 is finite, as the prime numbers that are less than 99 are finite.
Question 3.
State whether each of the following sets is finite or infinite:
(i) The set of lines that are parallel to the x-axis
(ii) The set of letters in the English alphabet
(iii) The set of numbers that are multiples 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 that are parallel to the x-axis is infinite, as the lines that are parallel to the x-axis are infinite.
(ii) The set of letters in the English alphabet is finite as it contains 26 elements.
(iii) The set of numbers that are multiples of 5 is infinite, as the multiples of 5 are infinite.
(iv) The set of animals living on the earth is finite as 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, as an infinite number of circles can pass through the origin.
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}, B = {d, c, b, a}
The order in which the elements of a set are listed is not significant.
Therefore, A = B
(ii) A = {4, 8, 12, 16}, B = {8, 4, 16, 18}
We know that 12 ∈ A but 12 ∉ B
Therefore, A ≠ B
(iii) A = {2, 4, 6, 8, 10}
B = {x: x is a positive even integer and x ≤ 10} = {2, 4, 6, 8, 10}
Therefore, A = B
(iv) A = {x: x is a multiple of 10}
B = {10, 15, 20, 25, 30,…}
We know that 15 ∈ B but 15 ∉ A
Therefore, A ≠ B
Question 5.
Are the following pair of sets equal? Give reasons.
(i) A = {2, 3}, B = {x: x is a 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 a solution of x2 + 5x + 6 = 0}
x2 + 5x + 6 = 0 can be written as x(x + 3) + 2(x + 3) = 0
By further calculation
(x + 2) (x + 3) = 0
So we get x = -2 or x = -3
Here A = (2, 3); B = (-2, -3)
Therefore, 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}
The order in which the elements of a set are listed is not significant.
Therefore, A = B
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:
We know that 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 can be written as 2 ∈ A, 2 ∉ C
Therefore, A ∉ C
3 ∈ B, 3 ∉ C, 3 ∉ F, 3 ∉ G, 3 ∉ H
B ≠ C, B ≠ E, B ≠ F, B ≠ G, B ≠ H
It can be written as
12 ∈ C, 12 ∉ D, 12 ∉ F, 12 ∉ G, 12 ∉ H
Therefore, C ≠ D, C ≠ E, C ≠ F, C ≠ G, C ≠ H
4 ∈ D, 4 ∉ E, 4 ∉ F, 4 ∉ G, 4 ∉ H
Therefore, D ≠ E, D ≠ F, D ≠ G, D ≠ H
Here, E ≠ F, E ≠ G, E ≠ H, F ≠ G, F ≠ H, G ≠ H
The order in which the elements of a set are listed is not significant.
B = D and E = G
Therefore, among the given sets, B = D and E = G.