State whether the following pairs of sets are equal or not:

(i) A = {2, 4, 6, 8, 10}, B = {even natural numbers}

(ii) A = {3, 5, 7, 9, 11, 13}, B = {odd natural numbers between 2 and 14}

(iii) A = {PUPPET}, B = {P, U, E, T}

(iv) A = {x | x is a letter in the word SOPHIA}, B = {x | x is a letter in the word MUMTAZ}

(v) A = {kids 5 metres tall}, B = {x : x ∈ N and 2x = 3}

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

B = {even natural numbers} = {2, 4, 6, 8, 10, 12, 14, ……}

The elements of A and B are not the same as B contains many more elements than A.

Hence, A ≠ B.

(ii) A = {3, 5, 7, 9, 11, 13}

The odd natural numbers between 2 and 14 are 3, 5, 7, 9, 11 and 13.

B = {odd natural numbers between 2 and 14} = {3, 5, 7, 9, 11, 13}

The elements of A and B are exactly the same.

Hence, A = B.

(iii) A = {PUPPET}

This set has only one element, namely the word "PUPPET".

B = {P, U, E, T}

This set has four elements P, U, E and T.

The elements of A and B are not the same.

Hence, A ≠ B.

(iv) A = {x | x is a letter in the word SOPHIA} = {S, O, P, H, I, A}

B = {x | x is a letter in the word MUMTAZ} = {M, U, T, A, Z}

The elements of A and B are not the same.

Hence, A ≠ B.

(v) A = {kids 5 metres tall}

There is no kid who is 5 metres tall, so A = { } i.e. A is an empty set.

B = {x : x ∈ N and 2x = 3}

2x = 3 ⇒ x = $\dfrac{3}{2}$, which is not a natural number.

So, B = { } i.e. B is also an empty set.

Both A and B have no elements.

Hence, A = B.