RBSE Solutions for Class 11 Maths Chapter 1 Sets Ex 1.2
Rajasthan Board RBSE Solutions for Class 11 Maths Chapter 1 Sets Ex 1.2 Textbook Exercise Questions and Answers.
RBSE Class 11 Maths Solutions Chapter 1 Sets Ex 1.2
Question 1.
Which of the following are examples of the null set:
(i) Set of odd natural numbers divisible by 2.
Answer:
Odd natural numbers are {1, 3, 5, 7, 9, 11, 13....}
We-know that no odd natural number is divisible by 2. So, this set has no element. Thus, it will be null set Φ.
(ii) Set of even prime numbers.
Answer:
We know that even prime number is 2 so this set can be written as {2} which contains one element. So, this set is not null set.
(iii) {x : x is a natural number, x < 5 and x > 7}
Answer:
Since natural numbers less than 5 and greater than 7 are not possible. So, this is an example of null set.
(iv) {y : y is a point common to any two parallel lines}
Answer:
We know that two parallel lines cannot meet so they will not have common point. Thus, given set will be null set.
Question 2.
Which of the following sets are finite or infinite :
(i) The set of months of a year.
Answer:
Since number of months in a year is 12, i.e., finite, so set of months of a year is finite.
(ii) { 1, 2, 3, ...............}
Answer:
Set { 1, 2, 3, .......................} is infinite because have infinite number of elements.
(iii) { 1, 2, 3, ............. 99,100}
Answer:
{1, 2, 3, ................ 99, 100} is finite set, since here number of elements are finite.
(iv) The set of positive integers greater than 100.
Answer:
Given set is infinite, since here number of elements are infinite.
(v) The set of prime numbers less than 99.
Answer:
Given set is finite, since prime number less than 99 are countable.
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.
Answer:
Given set is infinite since infinite parallel rays can be drawn parallel to x-axis.
(ii) The set of letters in the English alphabet.
Answer:
Given set is finite since number of letters in English alphabet is 26 which is finite.
(iii) The set of numbers which are multiple of 5.
Answer:
Given set is infinite, since there are many multiples of 5 as {5,10,15,20............}
(iv) The set of animals living on the Earth.
Answer:
Given set is finite, since animals on the Earth are countable.
(v) The set of circles passing through the origin (0,0).
Answer:
Given set is infinite, since infinite circles can be drawn from origin (0,0).
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....}
Answer:
(i) ∵ A = {a, b, c, d},B = {d, c, b, a}
Here each element of A occur in set B and each element of B occurs in set A.
Thus, A = B
(ii) ∵ A = {4, 8, 12, 16} B = {8, 4, 16, 18}
Here, 12 ∈ A but 12 ∉ B
18 ∈ B but 18 ∉ A
Thus, A ≠ B
(iii) ∵ A={2, 4, 6, 8, 10}
Writing set B is roster form
B = {2, 4, 6, 8, 10}
We see that both the sets have same number of elements.
Thus A = B
(iv) Since A = {10, 20, 30, 40..........} and B = {10, 15, 20, 25,....}. All the elements of B as 15,25, .......... are not occur in A.
Thus, A ≠ B
Question 5.
Are the following pair of sets equal? Give reasons.
(i) A = {2, 3}, B = { x: x is 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}
Answer:
(i) Since, set A and B have different elements.
So, pair of set is not equal.
Thus, A ≠ B
(ii) Since, set A and B have same elements. So, pair of sets is same.
Thus, 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}
Answer:
B and D are same, because both have same elements
B= {1,2, 3,4}, D = {3, 1,4,2}
Thus, B = D.
Similarly, E and G are same, because both have same elements.
E ={-1,1} and F = {1,-1}
Thus, E = G.
Any two set of the remaining sets are not same.
