1. Which of the following are examples of the null set:-

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

Example of Null Set.

(ii) Set of even prime numbers.

Not eg of null set.

(iii) {x:x is natural numbers, x < 5 and x < 7}.

Eg of Null Set.

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

Eg of Null Set.

2. which of the following sets are finite and infinite.

(i) The set of months in a year.

Finite.

(ii) {1, 2, 3,….}

Infinite.

(iii) {1, 2, 3, …., 99, 100}

Finite

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

Infinite.

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

Finite.

3. State whether each of the following set is finite or infinite:-

(i) The set of lines which are parallel to the x-axis.

Infinite. Because Infinite lines can be drawn parallel to x-axis.

(ii) The set of letters in English alphabet.

Finite. Because it is a set of 26 letters.

(iii) The set of numbers which are multiple of 5.

Infinite. Because there are infinite multiples of 5.

(iv) The set of animals living on earth.

finite. Because there are finite no. of animals living on earth.

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

Infinite. Because infinite circles can be drawn from origin (0, 0).

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 & x ≤ 10}

(iv) A = {x:x is multiple of 10}   B = {10, 15, 20, 25, 30, ……}

Sol:- (i) A = B

         (ii) A ≠ B

        (iii) A = B 

        (iv) A ≠ B.

5. Are the following pair of sets equal? give reasons

(i) A = B {2, 3}         B = {x:x is a solution of x² + 5x + 6 = 0}

No. Since x² + 5^x + 6 = 0

X² + 2x + 3x + 6 = 0

X (x+2) + 3 (x+2) = 0

(x+3) (x+2) = 0

-3, -2

As, value of A is positive. So, A ≠ B.

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

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

As, A = {FOLW}       B = {W, O, L, F}.

Since every element of A is in B and every element B is in A.

So, A = B

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 = {o, a}, G = {1, -1}, H = {0, 1}.

Equal Sets are B & D, E & G.