Answer whether the following statements are true or false. Give reasons.

(i) The set of even natural numbers less than 21 and the set of odd natural numbers less than 21 are equivalent sets.

(ii) If E = {factors of 16} and F = {factors of 20}, then E = F.

(iii) The set A = {integers less than 20} is a finite set.

(iv) If A = {x : x is an even prime number}, then set A is empty.

(v) The set of odd prime numbers is the empty set.

(vi) The set of squares of integers and the set of whole numbers are equal sets.

(i) True

Reason

The set of even natural numbers less than 21

A = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}

The set of odd natural numbers less than 21

B = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}

A and B both contains 10 elements. Hence they are equivalent sets.

(ii) False

Reason

E = {factors of 16}

Factors of 16 = 1, 2, 4, 8, 16

E = {1, 2, 4, 8, 16}

F = {factors of 20}

Factors of 20 = 1, 2, 4, 5, 10, 20

F = {1, 2, 4, 5, 10, 20}

Hence, E ≠ F

(iii) False

Reason

A = {integers less than 20}

A contains all negative numbers, 0, positive numbers less than 20.

A = {……………, -5, -4, -3, -2, -1, 0 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19}

Hence, A is infinite set.

(iv) False

Reason

A = {x : x is an even prime number}

A = {2}

Hence, A is not an empty set.

(v) False

Reason

Odd prime numbers = 3, 5, 7, 11, 17, …………….

A = {3, 5, 7, 11, 17, …………….}

Hence, it is not an empty set.

(vi) False

Reason

The set of squares of integers

M = {1², 2², 3², 4²,…………….}

M = {1, 4, 9, 16,…………….}

The set of whole numbers:

N = {0, 1, 2, 3, 4, …………….}

M ≠ N