A ={0} is a/an

Options

A. empty set
B. infinite set
C. singleton set
D. subset.

Answer

To determine the nature of the set A = {0}, we can analyze it step by step:

### Step 1: Identify the elements in the set
The set A contains only one element, which is 0.

**Hint:** Count the number of elements in the set to understand its classification.

### Step 2: Determine if the set is empty
An empty set is defined as a set that contains no elements at all. Since A contains one element (0), it is not an empty set.

**Hint:** Remember that an empty set is denoted by {} or ∅.

### Step 3: Check if the set is infinite
An infinite set has an uncountable number of elements. Since A contains only one element, it cannot be classified as an infinite set.

**Hint:** Think about how many elements you can count in the set.

### Step 4: Identify if the set is a singleton set
A singleton set is defined as a set that contains exactly one element. Since A = {0} contains exactly one element, it qualifies as a singleton set.

**Hint:** Recall the definition of a singleton set: it should have only one element.

### Step 5: Determine if the set is a subset
A subset is a set where all elements of the subset are also contained within another set. Since A = {0} is a set in itself, we cannot classify it as a subset without referencing another set.

**Hint:** A subset must be compared to another set to determine its relationship.

### Conclusion
Based on the analysis, the set A = {0} is a singleton set.

**Final Answer:** The correct classification of the set A = {0} is a singleton set.