Question

Set of even numbers which are not divisible by 2.

Answer 1

Answer:

Integers exactly divisible by 2 are called even; integers not divisible by 2 are called odd. numbers 1, 3, 5, 7, 9,...... 1001 are odd.

Answer 2

Since there exists no even number that is not divisible by 2 so the required set is empty or ∅.

Given:

The set of even numbers which are not divisible by 2.

To Find:

The set of even numbers which are not divisible by 2.

Solution:

To solve this problem, we will look at the properties of even numbers.

i) Even numbers are the numbers that are multiples of 2. Hence, every even number is divisible by 2.

ii) Even numbers have the general form 2m+2, where m is any integer.

iii) The set of even numbers are given by: {..., -4, -2, 0, 2, 4, 6, ...}

Hence, from the above properties, it is clear that there exists no even number that is not divisible by 2.

So the required set, which is the set of even numbers which are not divisible by 2, is empty or ∅.

∴ Since there exists no even number that is not divisible by 2, so the required set is empty or ∅.

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