1. State which of the following sets are empty and which are not?

(i) The set of lines passing through a given point.

(ii) Set of odd natural numbers divisible by 2.

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

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

(v) Set of even prime numbers.

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

(i) The set of months in a year.

(ii) {1, 2, 3, …, 99, 100}

(iii) The set of prime numbers smaller than 99.

(iv) The set of letters in the English alphabet.

(v) The set of lines that can be drawn are parallel to the X-Axis.

(vi) The set of numbers which are multiples of 5.

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

1. If A = {1, 2, 3, 4} and B = {1, 2, 3, 5, 6}, then find A ∩ B and B ∩ A. Are they equal?

2. If A = {0, 2, 4}, find A ∩ φ and A ∩ A. Comment.

3. If A = {2, 4, 6, 8, 10} and B = {3, 6, 9, 12, 15}, find A – B and B – A.

4. If A and B are two sets such that A ⊆ B then what is A ∪ B?

5. Let A = {x : x is a natural number}, B = {x : x is an even natural number}, C = {x : x is an odd natural number} and D = {x : x is a prime number}. Find A ∩ B, A ∩ C, A ∩ D, B ∩ C, B ∩ D and C ∩ D.

6. If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16} and D = {5, 10, 15, 20}, find (i) A – B (ii) A – C (iii) A – D (iv) B – A (v) C – A (vi) B – D (vii) B – C (viii) C – B (ix) C – D (x) D – B.

7. State whether each of the following statements is true or false. Justify your answers.

(i) {2, 3, 4, 5} and {3, 6} are disjoint sets.

(ii) {a, e, i, o, u} and {a, b, c, d} are disjoint sets.

(iii) {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.

(iv) {2, 6, 10} and {3, 7, 11} are disjoint sets.

1. Which of the following are sets? Justify your answer.

(i) The collection of all the months of a year beginning with the letter “J”.

(ii) The collection of ten most talented writers of India.

(iii) A team of eleven best cricket batsmen of the world.

(iv) The collection of all boys in your class.

(v) The collection of all even integers.

2. If A = {0, 2, 4, 6}, B = {3, 5, 7} and C = {p, q, r}, then fill the appropriate symbol, \( \in \) or \( \notin \) in the blanks.

(i) 0 … A

(ii) 3 … C

(iii) 4 … B

(iv) p … C

(v) 7 … B

(vi) 7 … A

3. Express the following statements using symbols.

(i) The element \( x \) does not belong to \( A \).

(ii) \( d \) is an element of the set \( B \).

(iii) \( 1 \) belongs to the set of Natural numbers.

(iv) \( 8 \) does not belong to the set of prime numbers \( P \).

4. State whether the following statements are true or false. Justify your answer.

(i) 5 \( \in \) set of prime numbers

(ii) S = {5, 6, 7} implies 8 \( \in \) S.

(iii) -5 \( \in \) \( \mathbb{W} \) where \( \mathbb{W} \) is the set of whole numbers.

(iv) \( \frac{11}{2} \in \mathbb{Z} \) where \( \mathbb{Z} \) is the set of integers.

5. Write the following sets in roster form.

(i) B = {x : x is a natural number smaller than 6}

(ii) C = {x : x is a two-digit natural number such that the sum of its digits is 8}

(iii) D = {x : x is a prime number which is a divisor of 60}

(iv) E = {x : x is an alphabet in BETTER}

6. Write the following sets in the set-builder form.

(i) {3, 6, 9, 12}

(ii) {2, 4, 8, 16, 32}

(iii) {5, 25, 125, 625}

(iv) {1, 4, 9, 16, 25, …, 100}

7. Write the following sets in roster form.

(i) A = {x : x is a natural number greater than 50 but smaller than 100}

(ii) B = {x : x is an integer, \( x^2 < 4 \)}

(iii) D = {x : x is a letter in the word “LOYAL”}

8. Match the roster form with set-builder form.

(i) {1, 2, 3, 6}

(ii) {2, 3}

(iii) {m, a, t, h, e, i, c, s}

(iv) {1, 3, 5, 7, 9}