List all the subsets of the following sets.

(i) B = {p, q}

(ii) C = {x, y, z}

(iii) D = {a, b, c, d}

(iv) E = {1, 4, 9, 16}

(v) F = {10, 100, 1000}

In each of the following, state whether A = B or not.

(i) A = {a, b, c, d}

B = {d, c, a, b}

(ii) A = {4, 8, 12, 16}

B = {8, 4, 16, 18}

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

B = {x: x is a positive even integer and x < 10}

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

B = {10, 15, 20, 25, 30, ….}

State the reasons for the following:

(i) {1, 2, 3, …., 10} ≠ {x: x ∈ N and 1 < x < 10}

(ii) {2, 4, 6, 8, 10} ≠ {x: x = 2n + 1 and x ∈ N}

(iii) {5, 15, 30, 45} ≠ {x: x is a multiple of 15}

(iv) {2, 3, 5, 7, 9} ≠ {x: x is a prime number}

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

(i) The set of lines passing through a 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.

Which of 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.