A set of odd natural numbers divisible by 2 is a null set (also known as an empty set).
This is because:
- Odd numbers are integers that cannot be divided evenly by 2. They always leave a remainder of 1 when divided by 2. Examples include 1, 3, 5, 7, and so on.
- Divisibility by 2 means that a number can be divided by 2 with no remainder. This is a characteristic of even numbers. Examples include 2, 4, 6, 8, and so on.
According to the provided reference from cuemath.com, "A set of odd natural numbers divisible by 2 is a null set because there is no odd number that is divisible by 2."
Therefore, since no odd number can ever be divisible by 2, the set that would contain such numbers has no elements, making it a null set, often denoted by the symbol ∅ or { }.
| Concept | Explanation |
|---|---|
| Odd Numbers | Integers not divisible by 2 (remainder of 1 when divided by 2) |
| Divisible by 2 | Ability to be divided by 2 with no remainder |
| Null Set (Empty Set) | A set containing no elements |
| Set of odd natural numbers divisible by 2 | This is an impossible condition to meet, resulting in an empty set. |
