# Â  Â  Â  Â  Â  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:Â xÂ is a natural numbers,Â xÂ < 5 andÂ xÂ > 7}

(iv) {y:Â yÂ is a point common to any two parallel lines}

Solution: (i)Â  Set of odd natural numbersÂ  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)Â {x:Â x is a natural number, Â  andÂ  } is a null set, a number cannot be both less than 5 and greater than 7.

(iv)Â {y:Â y is a point common to any two parallel lines} is a null set,Â  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 â€¦}

(iii) {1, 2, 3 â€¦ 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)Â  is an infinite set because it has an infinite number of natural numbers.

(iii)Â  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 theÂ 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)Â The set of lines which are parallel to theÂ x-axis is an infinite set.

(ii) The set of letters in the English alphabet is a finite set,Â  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,Â b,Â c,Â d}; B = {d,Â c,Â b,Â a}

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

(iii) A = {2, 4, 6, 8, 10}; B = {x:Â xÂ is positive even integer andÂ xÂ â‰¤ 10}

(iv) A = {x:Â xÂ is a multiple of 10}; B = {10, 15, 20, 25, 30 â€¦}

Solution:

(i)Â A = {a,Â b,Â c,Â d}; B = {d,Â c,Â b,Â a}

The order in which the elements of a set are listed is not significant.

Therefore, .

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

We know that 12 âˆˆ A but 12 âˆ‰ B.

Therefore,

(iii)Â A = {2, 4, 6, 8, 10};

B = {x:Â xÂ is a positive even integer andÂ xÂ â‰¤ 10} = {2, 4, 6, 8, 10}

Therefore,

(iv)Â A = {x:Â xÂ is a multiple of 10}

B = {10, 15, 20, 25, 30 â€¦}

We know that 15 âˆˆ B but 15 âˆ‰ A.

Therefore,

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

(i) A = {2, 3}; B = {x:Â xÂ is solution ofÂ x2Â + 5xÂ + 6 = 0}

(ii) A = {x:Â xÂ is a letter in the word FOLLOW}; B = {y:Â yÂ is a letter in the word WOLF}

Solution: (i) A = {2, 3}; B = {x:Â xÂ is solution ofÂ x2Â + 5xÂ + 6 = 0}

x2Â + 5xÂ + 6 = 0 can be written as

â‡’Â  x(xÂ + 3) + 2(xÂ + 3) = 0

â‡’Â  (xÂ + 2) (xÂ + 3) = 0

So, we get

xÂ = â€“2 orÂ xÂ = â€“3

Here,

A = {2, 3}; B = {â€“2, â€“3}

Therefore,

(ii) A = {x:Â xÂ is a letter in the word FOLLOW} = {F, O, L, W}

B = {y:Â yÂ 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 = {â€“1, 1}, F = {0,Â a}, G = {1, â€“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 = {â€“1, 1}; F = {0,Â a}

G = {1, â€“1}; H = {0, 1}

From above sets

B = D and E = G

Therefore, among the given sets, B = D and E = G.

Ex 1.1 ncert maths solution class 11