**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, **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 x≤10 }**

**(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 **Therefore A ****≠**** B**

**(iii).** A = {4, 2, 6, 10, 8}

B = {x: x is positive even integer and

= {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

**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

The equation given

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

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

Also,

2

**Therefore, A ****≠**** B**

Also, 3

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

Also,

12

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

Also,

4

**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.**