For the set of all natural numbers the universal set can bea)Set of all odd numbersb)Set of all even numbersc)Set of all integersd)Set of all prime numbersCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Yes because natural numbers come under integers

Answer

There can be 2 reasons to prove it correct option. 1. All natural no. are included in positive integers 2. All even ,odd,prime no. are also included in integers

Answer

First

universal set cannot be less than a given set hence the correct answer can't be option a,b,d

second

universal set at least be equal to the given set or contain more element than given set this is why for the set of natural number universal set can be set of all integers

Answer

As in the option c there are integers were as well as natural numbers. In another options there are only some of the elements. Hence it is option c.

Answer

Natural numbers are also lies in integers

Answer

Actually only option c has all the elements of natural number also no other option defines set of natural number as no one has all the elements of natural number except option c.

Answer

Set of all natural numbers as the universal set:
Natural numbers are a set of positive integers starting from 1 and continuing indefinitely. The set of all natural numbers is often denoted by the symbol 'N'.

Explanation:

Set of all integers:
- The set of all integers includes all whole numbers, both positive and negative, including zero.
- Natural numbers are a subset of integers since all natural numbers are also integers.
- Therefore, the set of all integers can be considered as the universal set for the set of all natural numbers.

Set of all odd numbers, even numbers, and prime numbers:
- Odd numbers are integers that are not divisible by 2, while even numbers are divisible by 2.
- Prime numbers are integers greater than 1 that have no divisors other than 1 and themselves.
- While these sets are related to natural numbers, they do not encompass all natural numbers and therefore cannot serve as the universal set for the set of all natural numbers.

Conclusion:
The set of all integers is the most inclusive set that contains all natural numbers as a subset. Therefore, the set of all integers is the appropriate universal set for the set of all natural numbers.

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