Class 11 Maths Ncert Solutions Ex 1.2

Class 11 Maths Ncert Solutions Chapter 1 Ex 1.2

Q.1: Which of the following given below is null set?

(i).  Set of odd natural numbers which is divisible by 2.

(ii).  Set of even numbers which are prime

(iii).  {x: x is a natural number, x<5 and x>7}

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

 

Answer:

(i).  A set of odd natural numbers which are divisible by 2 is a null set as none of the odd numbers is divisible by 2.

(ii).  A set of even prime numbers is not null set as there is number 2 which is prime and also divisible by 2.

(iii).  {x: x is a natural number, x<5 and x>7} is a null set as any number cannot be less than 5 and also greater than 7.

(iv).  {y: y is a point common to any two parallel lines} is a null set as parallel lines do not intersect. Therefore, there is no common point.

 

 

Q.2:  State whether the following sets are infinite or finite:

(i).  A set of months of a year.

(ii).  {1, 2, 3 ….}

(iii).  {1, 2, 3…99, 100}

(iv).  The set of positive integers which are greater than 100.

(v).  The set of prime numbers which are less than 99

 

Answer:

(i).  The set of months of a year has 12 elements. Therefore, it is a finite set.

(ii).  {1, 2, 3 ….} has infinite numbers in the set. Therefore, it is infinite set.

(iii).  {1, 2, 3…99, 100} has elements from 1 to 100. Therefore, it is finite set.

(iv).  The set of positive integers which are greater than 100 has infinite elements as there are infinite such elements. Therefore, it I infinite set.

(v).  The set of prime numbers which are less than 99 has finite numbers in this set which is less than 99. Therefore, it is finite set.

 

 

Q.3: State whether the following sets are infinite or finite:

(i).  The set of lines parallel to the x – axis.

(ii).  The set of letters in the vowels.

(iii).  The set of numbers multiple of 10.

(iv).  The set of humans living on Earth.

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

 

Answer:

(i).  The set of lines which are parallel to the x-axis has infinite elements. Therefore, it is an infinite set.

(ii).  The set of letters in the vowels has a finite element that is 5 elements. Therefore, it is a finite set.

(iii).  The set of numbers which are multiple of 5 has infinite elements. Therefore, it is an infinite set.

(iv).  The set of animals living on the earth has a finite number of elements. Therefore, it is finite set.

(v).  The set of circles passing through the origin (0, 0) has infinite elements as number of circles can pass through the origin. Therefore, it is an infinite set.

 

 

Q.4: In the following set given below, state whether A = B or not:

(i).  A = {w, x, y, z}

       B = {z, y, x, w}

(ii).  A = {5, 9, 13, 17}

        B = {9, 5, 17, 19}

(iii).  A = {4, 2, 6, 10, 8}

         B = {x: x is positive even integer and x10 }

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

          B = {10, 15, 20, 25, 30 …}

 

Answer:

(i).  A = {w, x, y, z}

B = {z, y, x, w}

Both the sets have same elements but the order is different. Therefore, A = B

(ii).   A = {5, 9, 13, 17}

B = {9, 5, 17, 19}

It can be seen that 13 A but 13 B. Therefore A B

(iii).  A = {4, 2, 6, 10, 8}

B = {x: x is positive even integer and x10 }

= {2, 4, 6, 8, 10}

Therefore, A = B

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

B = {10, 15, 20, 25, 30 …}

It can be seen that 15 B but 15 A.

Therefore A B

 

 

Q.5 In the following set given below, is the pair of sets equal?

(i). A = {3, 4}

      B = {y: y is solution of y2+5y+6=0}

 

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

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

 

Answer:

(i) A = {3, 4}

B = {y: y is solution of y2+5y+6=0}

The equation given y2+5y+6=0 can be solved as:

y (y + 3) + 2(y + 3) = 0

(y + 2) (y + 3) = 0

y = –2 or y = –3

Therefore, A = {2, 3} and B = {–2, –3}

Therefore, A  B

 

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

= {F, O, L, W}

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

= {W, O, L, F}

Both the sets have same elements but the order is different.

Therefore, A = B

 

 

Q.6: From the following sets, 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:

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}

We can see that:

8 A, 8 B, 8 D, 8 E, 8 F, 8 G and 8 H

Therefore, A B, A D, A E, A F, A G and A H

Also,

2 A and 2 C

Therefore, A  B

Also, 3 B, 3 C, 3 E, 3 F, 3 G and 3 H

Therefore, B C, B E, B F, B G, B H

Also,

12 C, 12 D, 12 E, 12 F, 12 G, 12 H

Therefore, C D, C E, C F, C G and C H

Also,

4 D, 4 E, 4 F, 4 G, 4 H

Therefore, D E, D F, D G, D H

Similarly, E ≠ F, E ≠ G, E ≠ H, F ≠ G, F ≠ H and G ≠ H

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

Therefore, B = D and E = G

Therefore, they are equal.

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