In set -builder form the null set is represented by

Options

A. `{}`
B. ` phi `
C. ` { x|x ne x |}`
D. `{ x| x ne =x|}`

Answer

To represent the null set in set-builder form, we can follow these steps:

### Step 1: Understand the Null Set
The null set, also known as the empty set, is a set that contains no elements. It is denoted by the symbol ∅ (phi) or by using curly brackets with no elements, i.e., {}.

### Step 2: Set-Builder Notation
Set-builder notation is a way to describe a set by stating the properties that its members must satisfy. It is generally written in the form:
\[ \{ x \, | \, P(x) \} \]
where \( P(x) \) is a property that elements \( x \) must satisfy to be included in the set.

### Step 3: Constructing the Null Set in Set-Builder Form
To express the null set in set-builder notation, we need to define a property that cannot be satisfied by any element. A common way to do this is to state that an element \( x \) does not equal itself, which is always false. Therefore, we can write:
\[ \{ x \, | \, x \neq x \} \]
This indicates that there are no elements \( x \) that satisfy the condition \( x \neq x \).

### Conclusion
Thus, the null set in set-builder form can be represented as:
\[ \{ x \, | \, x \neq x \} \]