Question

If A = {1, 2, 3, ….} and N is a set of natural numbers, check whether A and N are equal?

Answer 1

natural numbers start from 1 and extend to the last(unknown)
So, the set of natural numbers is,
N = {1,2,3, .....}
&
A = {1,2,3, .....}

By observing both, A = N; i.e.,both sets are equal

Answer 2

Set A is equal to Set N

Given:

Set A = {1,2,3,...}

Set N = set of natural numbers

To find:

To check whether A = N

Solution:

To check whether set A = set N we have to check if these two are equal sets.

Two sets A and B are said to be equal only if each element of set A is also the element of set B.

Here,

N = set of natural number

Natural numbers are numbers beginning from 1 and going up to ∞

∴ N = {1,2,3,...}  ----------> (1)

We are given,

A = {1,2,3,...}   ------------> (2)

From (1) and (2),

We can see that the elements present in set A are the same as in set N and are in the same position. The dots(...) symbolize that these sets go up to infinity. ∴ They are equal sets

Hence Set A = Set N

                                                                                                              Proved

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