Which of the following sets is a null set?
1. X = {x | x= 9, 2x = 4}
IL Y = {x | x= 2x.x # 0}
III. Z = {x | x-8 = 4}
A. I and II only
B. I, II and III
C. I and III only
D. II and Ill only
Answers
Answer:
Answer
Empty set is a set which does not contains any element.
i] Set of all even natural numbers divisible by 5
→ Not a Empty set, e.q. 10, seven natural number &
divisible by 5.
ii] Set of all even prime number
→ not a Empty set e.q. 2 is even prime number
iii] {x:x
2
−2=0 & x is rational }
→ not a Empty set, e.q. x=2 satisfy which is a
rational number.
iv] {x:x is a natural number x < 8 & x > 12 }
→ It is a empty set because if a natural number is less
than 8, then it cannot be greater than 12.
v] {x:x is a point common to any two parallel lines }
→ A empty set because there will be no common
point between two parallel lins.
So (iv) & (v) are examples of empty of empty sets.
A) I and II only
- In I it is given the condition that x = 9, 2x = 4 which means x = 9, x= 2 but x can't have both the values, therefore, no values of x satisfy the condition
Hence it is a null set.
- In II x = 2x, means 1= 2 but this is not true for any value of x
hence it is a null set
- In III x-8= 4, that is x = 12, therefore there is a value of x which satisfy the condition.
Hence it is not a null set.