Question

(3) Which of the following are empty sets ? why? (i) A= {al a is a natural number smaller than zero.} (ii) B= {x x = 0; (iii) C = {x | 5 x - 2 = 0, x € N}​

Answer 1

(i) A= {a l a is a natural number smaller than zero.}

→ A = { }

→Natural numbers are {1,2,3,4,5,...}

→There is no natural number less than zero

→It is an empty set

ii) B= {x | x²= 0}

→ x² =0

= x =√0

= x =0

→B= {0}

→It is not an empty set

(iii) C = {x | 5 x - 2 = 0, x € N}

→ 5x-2= 0

= 5x= 2+0

= x = 2/5

= 2/5

= 2/5 is not a natural number

= C= { }

→It is an empty set