Sets Class 11 Exercise 1.2 Solution 

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), (iii) and (iv) are null sets

2. Which of the following sets are finite or infinite

(i) The set of months of a year

Solution. This is a finite set.

(ii) {1, 2, 3, . . .}

Solution. This is an infinite set.

(iii) {1, 2, 3, . . .99, 100}

Solution. This is a finite set.

(iv) The set of positive integers greater than 100

Solution. This is a finite set.

(v) The set of prime numbers less than 99

Solution. This is an infinite set.

3. State whether each of the following set is finite or infinite:

(i) The set of lines which are parallel to the x-axis.

Solution. This is an infinite set.

(ii) The set of letters in the English alphabet.

Solution. This is a finite set.

(iii) The set of numbers which are multiple of 5

Solution. This is an infinite set.

(iv) The set of animals living on the earth

Solution. This is an infinite set.

(v) The set of circles passing through the origin (0,0)

Solution. This 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 }

Solution. A=B as set A and B have exactly same elements.

(ii) A = { 4, 8, 12, 16 } B = { 8, 4, 16, 18}

Solution. A≠B since element (12) is in set A but not in A.

(iii) A = {2, 4, 6, 8, 10} B = { x : x is positive even integer and x ≤ 10}

Solution. A=B (writing set B in roster form you can see set B is exactly same as set A.

(iv) A = { x : x is a multiple of 10}, B = { 10, 15, 20, 25, 30, . . . }

Solution. A≠B clearly element 15€B but it is not a multiple of 10 i.e., it is 15€A

5. Are the following pair of sets equal ? Give reasons.

(i) A = {2, 3}, B = {x : x is solution of x² + 5x + 6 = 0}

Solution. No, A≠B since solution of x² + 5x + 6 = 0 are -2,-3 i.e., B={-2,-3} , Clearly A≠B.

(ii) A = { x : x is a letter in the word FOLLOW}

B = { y : y is a letter in the word WOLF}

Solution. Clearly A={FOLW} =B, Thus A=B.

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. Clearly B=D and E=G.