Question

If 4 is removed from the set of whole numbers, is the set of whole numbers closed with respect to addition?

Answer 1

No....Because in any case if you take out a number, then it's place will be empty...So if you want to take out 4 from 8 (just an example), how can we do it ?

Hope it helps you!!!

Answer 2

The given set is not closed with respect to addition.

Given:

Number 4 is removed from the set of whole numbers.

To Find:

Whether the set of the whole number without 4 is closed under addition.

Solution:

Let S be the set of the whole number without the number 4.

A set is said to be closed under addition only if the addition of any two numbers also belongs to the set.

We know that 2 is a whole number.

⇒ 2 ∈ S

But the addition of 2+2=4∉S

addition of two numbers from the set does not belong to the set S.

Therefore, The given set is not closed with respect to addition.

#SPJ2

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