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}
(i) Odd numbers: An odd number is defined as an integer which is not a multiple of 2.
The set of odd numbers contains numbers like { 1 , 3 , 5 , 7 , 9.... } , where none of the numbers are divisible by 2 . Therefore, set of odd numbers which are divisible by 2 is a null set.
(ii) Prime number: Prime number is defined as a number that is divisible by 1 and that number itself.
Some examples of prime numbers are 2 , 3 , 5 , 7 , 11... .
Set of even prime numbers is not an example of a null set, as 2 is an even prime number.
(iii) The given set is { x : x is a natural number , x < 5 and x > 7 } . The given set should contain numbers which are less than 5 and greater than 7 .
As there is no number which is both less than 5 and greater than 7 , hence the given set will have no element in it and therefore, is also an example of a null set.
(iv)Parallel lines: Parallel lines are defined as the lines which never cut each other at any point.
Thus, a set whose elements are common points between the parallel lines has no element. Therefore, it is also an example of a null set.
(i) Odd numbers: An odd number is defined as an integer which is not a multiple of 2.
The set of odd numbers contains numbers like
(ii) Prime number: Prime number is defined as a number that is divisible by
Some examples of prime numbers are
Set of even prime numbers is not an example of a null set, as
(iii) The given set is
As there is no number which is both less than
(iv)Parallel lines: Parallel lines are defined as the lines which never cut each other at any point.
Thus, a set whose elements are common points between the parallel lines has no element. Therefore, it is also an example of a null set.
