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

Options

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

Answer

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

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

### Step 2: Use the formula for the number of subsets
The total number of subsets of a set with \( n \) elements is given by the formula \( 2^n \).

### Step 3: Calculate the total number of subsets
Using \( n = 3 \):
\[ \text{Total subsets} = 2^3 = 8 \]

### Step 4: Determine the number of proper subsets
A proper subset 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:
\[ \text{Proper subsets} = 2^n - 1 = 8 - 1 = 7 \]

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

### Final Answer
The correct option is \( C) 7 \).

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