Referring to the AP Inter 1st Year Maths Study Material Chapter 1 Sets Exercise 1b Solutions makes it easier to understand complex problems.
AP Inter 1st Year Maths Sets Solutions Exercise 1b
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 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 divisible by 2 is a null set because no odd number is divisible by 3.
ii) Set of even prime numbers is not a null set because 2 is an even prime number.
iii) {x : x is a natural numbers, x < 5 & x > 7}isa null set.
iv) {y : y is a point common to any two parallel lines} is a null set.
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 a finite set because it has 12 elements.
ii) {1, 2, 3, ……..} is an infinite set because it has infinite number of natural numbers.
iii) Given set is a finite set because it has 100 elements.
iv) Given set is an infinite set because it has infinite elements.
v) Given set is a finite set because prime numbers < 99 are finite.
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 lines parallel to the X-axis are infinite.
ii) The set of letters in the English alphabet is a finite set because it has 26 elements.
iii) The set of numbers which are multiples of 5 is an infinite set because multiples of 5 are infinite in numbers.
iv) The set of animals living on the earth is a finite set because animals living on the earth is finite.
v) The set of circles passing through the origin (0, 0) is an infinite set because the number of circles passing through the origin is infinite.
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 a positive even integer and x < 10}
iv) A = {x : x is a multiple of 10} B = {10, 15, 20, 25, 30, ….}
Solution:
i) A = B because every element in A is element in B and every element in B is element in A.
ii) A ≠ B because 12 ∈ A but 12 ∉ B.
iii) A = {2, 4, 6, 8, 10}, B = {2, 4, 6, 8, 10} ∴ A = B
iv) A = {10, 20, 30, …………}, B = {10, 15, 20, 25, 30, …….}
A ≠ B because 15 ∈ B, but 15 ∉ A.
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} = {-2, -3}
B = {-2, -3} ∴ A ≠ B
ii) A = {F, O, L, W}, B = [W, O, L, F} ∴ 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:
Two sets are equal if they contain exactly the same elements, regardless of order.
B = D, E = G.