11th NCERT Sets Exercise 1.2 Questions 6

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Question (1)

Which of the following are examples of the null set(i) Set of odd natural numbers divisible by 2

Solution

oddd numbers not divisible by 2. so it is null set.(ii) Set of even prime numbers

Solution

A = {2} , so not a null set.(iii) {x:x is a natural numbers, x < 5 and x > 7 }

Solution

There is no natural nuber which is less than 5 and greater than 7. So yes it is a null set.(iv) {y:y is a point common to any two parallel lines}

Solution

parallel lines do not have any common point. so it is a null set.Question (2)

Which of the following sets are finite or infinite(i) The set of months of a year

Solution

As in a year there are only 12 months. So it is finite set.(ii) {1, 2, 3 …}

Solution

It is infinite set.(iii) {1, 2, 3 … 99, 100}

Solution

As the numbers upto 100 has to write, os it is finite set.(iv) The set of positive integers greater than 100

Solution

Numbers are greater than 100 upto which is not mention so it is infinite set.(v) The set of prime numbers less than 99

Solution

As the numbers upto 99 , so if is finite set.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

Solution

We can draw infinite lines parallel to x axis. So it is infinite set.(ii) The set of letters in the English alphabet

Solution

In English there are 26 alphabets. so it is finite set.(iii) The set of numbers which are multiple of 5

Solution

We have infinite numbers which are multiple of 5, so it is infinite set.(iv) The set of animals living on the earth

Solution

There are infinite number of animals on earth. So it is finite set.(v) The set of circles passing through the origin (0, 0)

Solution

We can draw infinite circles passing through the (0, 0). So set is infinite set.Question (4)

In the following, state whether A = B or not: (i) A = {a, b, c, d}; B = {d, c, b, a}Solution

All elements of A and B are equal. So set A = B.(ii) A = {4, 8, 12, 16}; B = {8, 4, 16, 18}

Solution

All elements of A and B are not equal. So set A ≠ B.(iii) A = {2, 4, 6, 8, 10}; B = {x: x is positive even integer and x ≤ 10}

Solution

B = { 2, 4, 6, 8, 10}. All elements of set A and set B are equal. So A = B.(iv) A = {x: x is a multiple of 10}; B = {10, 15, 20, 25, 30 …}

Solution

A = { 10, 20, 30, .....} . All elements of set A and set B are not equal. So A ≠ B.Question (5)

Are the following pair of sets equal? Give reasons. (i) A = {2, 3}; B = {x: x is solution of xSolution

When we solve the quadratic equation we get roots as -3, -2.B = { -3, -2 } .

Elements ot set A and set B are different, so A ≠ B.

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

Solution

A = { F, O, L, W} , B = { W, O, L, F }all elements of set A and set B are equal.

So 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

All elements of set B and set D are equal, so B = D.All elements of set E and set G are equal, so E = G.