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Exercises · Q11

Q.Classify each of the following as empty, singleton or finite:

(i) {x:x∈N,3<x<4}\{x : x \in \mathbb{N}, 3 < x < 4\}
(ii) the set of even prime numbers
(iii) {x:x∈N,x≤100}\{x : x \in \mathbb{N}, x \le 100\}.
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(i) We need a natural number strictly between 3 and 4. There is no such integer (natural numbers are whole numbers, and nothing whole lies strictly between 3 and 4). So the set is empty, ∅\emptyset.

(ii) A prime number's only positive divisors are 1 and itself. Among even numbers, only 22 has this property — every other even number is divisible by 2 as well as some other number, so it has more than two divisors. So the set of even primes is {2}\{2\}, a singleton set. …

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