If A={a,b,c}, then what is the number of proper subsets of A?

Options

A. 5
B. 6
C. 7
D. 8

Explanation

To find the number of proper subsets of the set \( A = \{a, b, c\} \), we can follow these steps:

### Step 1: Determine the number of elements in set A.
The set \( A \) has three elements: \( a, b, c \).
- **Number of elements in A**: \( n = 3 \)

### Step 2: Calculate the total number of subsets of A.
The total number of subsets of a set with \( n \) elements is given by the formula \( 2^n \).
- For our set \( A \):
\[ \text{Total subsets} = 2^n = 2^3 = 8 \]

### Step 3: Identify the number of proper subsets.
A proper subset of a set is any subset that is not equal to the set itself. Therefore, to find the number of proper subsets, we subtract 1 from the total number of subsets (to exclude the set itself).
- Thus, the number of proper subsets is:
\[ \text{Proper subsets} = \text{Total subsets} - 1 = 8 - 1 = 7 \]

### Conclusion:
The number of proper subsets of the set \( A = \{a, b, c\} \) is \( 7 \).

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