Which of the following are examples of the null set?
(i) Set of odd natural numbers divisible by 2
(ii) Set of even prime numbers
(iii) {x : x is a natural numbers, x 7}
(iv) {y : y is a point common to any two parallel lines}
Answers
Answer:
(i) Given: Set of odd natural numbers divisible by 2.
As we know set is a collection of well defined objects.
Let we represent the given set in roaster form:
⇒ Set of odd natural numbers divisible by 2 is {ϕ}.
Because no odd natural number can be divided by 2. Hence, it is a null set.
(ii) Given: Set of even prime numbers.
As we know set is a collection of well defined objects.
Let we represent the given set in roaster form:
⇒ Set of even prime numbers is {2}.
Because 2 is an even prime number. Hence, it is not a null set.
(iii) Given: {x : x is a natural numbers, x < 5 and x > 7}
As we know set is a collection of well defined objects.
Let we represent the given set in roaster form:
⇒ {x : x is a natural numbers, x < 5 and x > 7} is {ϕ}.
Because no number can be simultaneously less than 5 and greater than 7.Hence, it is a null set.
(iv) Given: {y : y is a point common to any two parallel lines}
As we know set is a collection of well defined objects.
Let we represent the given set in roaster form:
⇒ {y : y is a point common to any two parallel lines} is {ϕ}.
Because two parallel lines never meet at any of the point so they don’t have any common point. Hence, it is a null set