Chapter 1: Sets

Exercise

Question

Question: 3 (v)

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Taking the set of natural numbers as the universal set, write down the complements of the following sets:

(v) {x : x is a natural number divisible by 3 and 5}

Answer

1
Find the complement of the given set by finding the elements of the universal set of numbers that are not elements of the given set.
Answer: {x : x $∈$ N, x is not divisible by 3 or not divisible by 5} or {x : x $∈$ N, x is not a multiple of 15}
Reason: A natural number that is divisible by both 3 and 5 is a multiple of 15. Therefore, after removing the multiples of 15, only the numbers that are not multiples of 15 remain.
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