Monday 7 April 2014

Which of the following are examples of the null set

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
(i)A there is no odd number which is divisible by 2.
Hence, set of odd natural numbers divisible by 2 is a null set.
(ii)2 is an even prime number.
Hence set of even prime numbers is not a null set.
(iii) There is no number which is less than 5 and greater than 7.
Hence, {x: x is a natural number, x < 5 and x > 7} is a null
(iv) Parallel lines never intersect each other.
Hence, {y: y is a point common to any two parallel lines} is a null set.

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