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Question -

Which of the following are examples of empty set?
(i) Set of all even natural numbers divisible by 5.
(ii) Set of all even prime numbers.
(iii) {x: x2тАУ2=0 and x is rational}.
(iv) {x: x is a natural number, x < 8 and simultaneously x > 12}.
(v) {x: x is a point common to any two parallel lines}.



Answer -

(i) All numbers ending with 0. Except 0 is divisible by 5 and are even natural number. Hence it is not an example of empty set.
(ii) 2 is a prime number and is even, and it is the only prime which is even. So this not an example of the empty set.
(iii) x2 тАУ 2 = 0, x2 = 2, x = ┬▒ тИЪ2 тИИ N. There is not natural number whose square is 2. So it is an example of empty set.
(iv) There is no natural number less than 8 and greater than 12. Hence it is an example of the empty set.
(v) No two parallel lines intersect at each other. Hence it is an example of empty set.

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