Question

Use complete sentences to describe why Set A = { X | X is an even whole number between 0 and 2} = ∅

Answer 1

Basically Set A has all the even whole numbers between 0 and 2
and Set A is empty


that is because
any even number can be represented as 2n where n is an integer

find 2n where n is an integer and it is between 0 and 2
0<2n<2
divide both sides by 2
0<n<1
so n must be between 0 and 1
but that makes it not an integer, integers are like -3,-2,-1,0,1,2,3, they can't be fractions or decimals


it is because there are no even whole numbers between 0 and 2

Answer 2

Consider the Set A = {X | X is an even whole number between 0 and 2 } = $\Phi$.

Since, whole numbers are the set of numbers starting from zero upto infinity.

Even numbers are the numbers which are exactly divisible by '2'.

So, we have to find the even whole number between 0 and 2.

Since, only '1' is a whole number between 0 and 2 which is not an even number as '1' is not divisible by '2'.

Therefore, there is no even whole number between 0 and 2.

So, this set is empty.

Therefore, A = { X | X is an even whole number between 0 and 2} =  $\Phi$