Question

Match each of the sets on the left in the roster form with the same set on the right described in the set builder form: 

i.{A,P,L,E} i. {x:x + 5 = 5, x z} 

ii.{5,- 5} ii. {x:x is a prime natural number and a divisor of 10} 

iii. {0} iii. {x:x is a letter of the word “RAJASTHAN”} 

iv. {1,2,5,10} iv. {x:x is a natural and divisor of 10} 

v. {A,H,j,R,S,T,N} v. {x:x² – 25 = 0} 

vi.{2,5} vi. {x:x is a letter of word “APPLE”}

Answer 1

When we are dealing with the set builder - roster form match the following it is always better to go in the direction in which we need to convert set builder to roster rather than roster to set builder. 

For i. {x:x + 5 = 5, x z} 

X is such that x+5 = 5 

⇒ x = 5 - 5 

⇒ x = 0 

Roster form = {0} 

i.e third option 

For ii. {x:x is a prime natural number and a divisor of 10} 

All natural numbers that are divisor of 10 are = 1,2,5,10 

Numbers that are prime are = 2,5 

Roster form = {2,5} 

i.e. sixth option. 

For iii. {x:x is a letter of the word “RAJASTHAN”} 

All letters means no letter should be repeated 

RAJASTHAN = R,A,J,S,T,H,N 

∴ Roster form will be {A,H,J,R,S,T,N} 

i.e. fifth option 

For iv. {x:x is a natural and divisor of 10} 

All natural numbers that are divisor of 10 are = 1,2,5,10. 

Roster form= {1,2,5,10} 

i.e. Fourth option. 

For v. {x:x² – 25 = 0} 

X²-25 = 0 

X =√25 

X = ± 5. 

∴ Roster form will be {5,- 5} 

i.e. second option 

for vi. {x:x is a letter of word “APPLE”} 

All letters means no letter should be repeated 

APPLE = A,P,L,E 

∴ Roster form will be {A,E,L,P} 

i.e. first option.