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, x7}(iv) {y: y is a point common to any two parallel lines}

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

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Solution: A Null set is a set that doesn′t contain any element. Here,(i) Set of odd natural numbers divisible by 2:There can′ be any odd number that is divisible by 2. So, this set will not have any element. It is a Null set. (ii) Set of even prime numbers: 2 is the only even number that is also prime number. So, this set contain a single elemnt that means it is not a Null set.(iii) {x: x is a natural numbers,x7}: It is not possible a natural number is less than 5 and greater than 7. So, this is a Null set.(iv){y: y is a point common to any two parallel lines}:Two parallel lines always remain distant with each other with a constant distance. So, there can not be a common points between them.This set also doesn′t contain any element.Thus, this set is also a Null set.

Question Text	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}
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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}

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