Which of the following are examples of the null set Set of odd natural numbers divisible by 2

Question

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 < 5 and x > 7 }
(iv) {y:y is a point common to any two parallel lines}

Answer 1

(i) A set of odd natural numbers divisible by 2 is a null set because no odd number is divisible by 2.
(ii) A set of even prime numbers is not a null set because 2 is an even prime number.
(iii) {x: x is a natural number, x < 5 and x > 7} is a null set because a number cannot be simultaneously less than 5 and greater than 7.
(iv) {y: y is a point common to any two parallel lines} is a null set because parallel lines do not intersect. Hence, they have no common point.