Identify the null sets among the following
A = { x: x is a whole number , ` x lt 1`}

Answer

To identify whether the set \( A = \{ x : x \text{ is a whole number}, x < 1 \} \) is a null set, we will follow these steps:

### Step 1: Understand the definition of a null set
A null set (or empty set) is a set that contains no elements.

**Hint:** Remember that a null set is denoted by \( \emptyset \) or \( \{ \} \).

### Step 2: Identify the conditions for set \( A \)
The set \( A \) is defined as containing whole numbers that are less than 1.

**Hint:** Whole numbers are non-negative integers starting from 0 (i.e., 0, 1, 2, 3, ...).

### Step 3: List the whole numbers less than 1
The whole numbers less than 1 are:
- 0 (since it is a whole number and is less than 1)
- 1 (not included because it is not less than 1)
- Any whole number greater than 1 (not included)

**Hint:** Think about the whole numbers starting from 0 and see which ones meet the condition.

### Step 4: Determine the elements of set \( A \)
From the above reasoning, the only whole number that is less than 1 is 0. Therefore, the set \( A \) can be written as:
\[ A = \{ 0 \} \]

**Hint:** Check if there are any other whole numbers that satisfy the condition.

### Step 5: Count the elements in set \( A \)
Set \( A \) contains one element, which is 0. Since it has one element, it is not an empty set.

**Hint:** A set with at least one element cannot be a null set.

### Conclusion
Since set \( A \) contains the element 0, it is not a null set.

**Final Answer:** \( A \) is not a null set.

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