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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}

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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.

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