NCERT Solutions Class 11 Maths
The NCERT Solutions in English Language for Class 11 Mathematics Chapter – 1 Sets Exercise 1.2 has been provided here to help the students in solving the questions from this exercise.
Chapter 1 (Sets)
Chapter : 1 Sets
- NCERT Class 11 Maths Solution Ex – 1.1
- NCERT Class 11 Maths Solution Ex – 1.3
- NCERT Class 11 Maths Solution Ex – 1.4
- NCERT Class 11 Maths Solution Ex – 1.5
- NCERT Class 11 Maths Solution Ex – 1.6
| Exercise – 1.2 |
1. Which of the following are examples of the null set?
(i) Set of odd natural numbers divisible by 2
Solution – Yes, this is a null set because three is no odd natural number divisible by 2.
Note – A set which does not contain any element is called the null set.
(ii) Set of even prime numbers
Solution – No, this is not a null set because 2 is an even number which is prime.
(iii) {x: x is a natural numbers, x < 5 and x > 7}
Solution – Yes, this is a null set because three is no natural number which is less than 5 and greater than 7.
(iv) {y: y is a point common to any two parallel lines}
Solution – Yes, this is a null set because two parallel lines have no points in common because they do not intersect.
2. Which of the following sets are finite or infinite?
(i) The set of months of a year
Solution – This is a finite set because there is only 12 months in a year.
(ii) {1, 2, 3 …}
Solution – This is an infinite set because there will always be a new number if we add 1 to the previous number, or we can say that it is a set of natural numbers and there are infinite natural numbers.
(iii) {1, 2, 3 … 99, 100}
Solution – This is a finite set because there is only 100 numbers in the set.
(iv) The set of positive integers greater than 100
Solution – This is an infinite set because there are infinite positive integers greater than 100 which can be generated by adding 1 to the previous number.
(v) The set of prime numbers less than 99
Solution – This is a finite set because prime numbers which are less than 99 are finite.
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 – Infinite. We can draw infinite parallel lines with respect to the x-axis.
(ii) The set of letters in the English alphabet
Solution – Finite. There are only 26 letters in the English alphabet.
(iii) The set of numbers which are multiple of 5
Solution – Infinite. There are infinite numbers which are multiple of 5 namely {5, 10, 15 ….. }
(iv) The set of animals living on the earth
Solution – Finite. The animals Living on the earth can be counted they are not infinite.
(v) The set of circles passing through the origin (0, 0)
Solution – Infinite. We can draw infinite number of circles passing through the origin with different radius.
4. In the following, state whether A = B or not:
(i) A = {a, b, c, d}; B = {d, c, b, a}
Solution – Yes. Every element of A is also an element of B and every element of B is also an element of A namely {a, b, c, d}.
(ii) A = {4, 8, 12, 16}; B = {8, 4, 16, 18}
Solution – No. 12 is an element that is present in A but not in B and similarly 18 is an element present in B not in A.
(iii) A = {2, 4, 6, 8, 10}; B = {x: x is positive even integer and x ≤ 10}
Solution – Yes. If we define set B it can be written like this {2, 4, 6, 8, 10} and therefore every element of A is also an element of B and every element of B is also an element of A.
(iv) A = {x: x is a multiple of 10}; B = {10, 15, 20, 25, 30 …}
Solution – No. If we define B we can clearly see that {-40, -30, -20, -10, 0}. All these numbers are also multiples of 10, and they are not in set B. Hence A ≠ B.
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.
By solving the equation x2 + 5x + 6,
x2 + 5x + 6 = 0
x2 + 2x + 3x + 6 = 0
(x + 2)(x + 3) = 0
x = -2, -3
Now it is clear that B can be defined as {-2, -3}.
Now -2, -3 are not in A and also 2, 3 is not in set B. Hence A ≠ B.
(ii) A = {x: x is a letter in the word FOLLOW}; B = {y: y is a letter in the word WOLF}
Solution – Yes.
It is clear that A can be defined as {F, O, L, W} an if we define B, {F, O, L, W}. Now it is clear that every element of A is also an element of B and every element of B is also an element of A namely {W, O, L, F}.
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 –
B = D & E = G.
Note: Two sets A and B are said to be equal if they have exactly the same elements.
For A, 8∈ A, but 8∉ B,8∉ B,8∉ D,8∉ E, 8∉ F,8∉ G,8∉ H,
Hence, A is not equal to B, D, E, F, G, H.
Also, 2∈ A, but 2∉ C Hence A, ≠ C.
For B, 2∈ B, but 2∉ C,2∉ E,2∉ F,2∉ G, 2∉ H.
Hence, B is not equal to C, E, F, G, H.
Also, Every element of B can be found in D namely {1, 2, 3, 4} and vice-versa is also true. Hence B = D.
For C, 14∈ C, but 14∉ D,14∉ E,14∉ F,14∉ G, 14∉ H.
Hence C is not equal to D, E, F, G, H.
For D, 2∈ D, but 12∉ E,2∉ F,2∉ G, 2∉ H.
Hence D is not equal to E, F, G, H.
For E, -1∈ E, but -1∉ F, -1∉ H.
Hence E is not equal to F, H.
Also, Every element of E can be found in G namely {-1, 1} and vice-versa is also true. Hence E = G.
For F, 0∈ F, but 0∉ G, 0∉ H.
Hence F is not equal to G, H.
For G, -1∈ G, but -1∉ H.
Hence G is not equal to H.
So, we can observe that only B = D & E = G.
