Question

Decide which of the following are equal sets and which are not ? Justify your answer.

 A= {x | 3x – 1 = 2}

 B = {x | x is a natural number but x is neither prime nor composite}

 C = {x | x e N, x < 2}

Answer 1

A = {x | 3x – 1 = 2}

Here, 3x – 1 = 2 

∴ 3x = 3 

∴ x = 1 

∴ A = {1} …(i)

B = {x | x is a natural number but x is neither prime nor composite} 

1 is the only number which is neither prime nor composite, 

∴ x = 1 

∴ B = {1} …(ii)

C = {x | x G N, x < 2}

1 is the only natural number less than 2.

∴ x = 1 

∴ C = {1} …(iii)

∴ The element in sets A, B and C is identical. …

[From (i), (ii) and (iii)] 

∴ A, B and C are equal sets