Which of the following are examples of the null set?(i) Set of odd | Filo
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Class 11

Math

Co-ordinate Geometry

Sets

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Which of the following are examples of the null set?
(i) Set of odd natural numbers divisible by
(ii) Set of even prime numbers
(iii) \left \{ x : x \text { is a natural numbers, x < 5x > 7}\right \}\left \{ y : y \text { is a point common to any two parallel lines}\right \}$$

Solution: (i) A set of odd natural numbers divisible by is a null set because no odd number is divisible by .

(ii) .
A set of even prime numbers is not a null set because is an even prime number.

(iii) is a null set because a number cannot be simultaneously less than and greater than .

(iv) is a null set because parallel lines do not intersect. Hence, they have no common point.
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