Monday, April 7, 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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