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) $$\{x:x\text{is a natural numbers,}\text{x < 5}\text{and}\text{x > 7}\}$$
(iv) $$\{y:y\text{is a point common to any two parallel lines}\}$$

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