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Which of the following are the 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 lt 5 and x gt 7`} (iv) {y : y is a point common to any two parallel lines}. |
Answer» (i) Odd natural numbers are 1,3,5,7,9,11,…. None of these numbers is divisible by 2 `:.` Set of odd natural number divisible by 2 = empty set `= phi` (ii) Collection of prime natural numbers `= 2,3,5,11,13,..` `rArr` Set of even prime natural numbers = {2} Therefore, the set of even prime natural numbers is not an empty set (iii) {x : x is a natural number `x lt 5 and x gt 7`} = a natural number which is smaller than 5 and greater than 7 `because` No such numbere is possible Thus, {x : x is natural number, `x lt 5 and x gt 7`} is an empty set (iv) {y : y is a point common to any two parallel lines} `because` There is no common point in two parallel lines. therefore, {y : y is a point common to any two parallel lines} is an empty set. |
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