If A=(1,2,3,4) then how many subsets of A contain the elements 3?

Options

A. 24
B. 28
C. 8
D. 16

Explanation

To find how many subsets of the set \( A = \{1, 2, 3, 4\} \) contain the element \( 3 \), we can follow these steps:

### Step 1: Identify the total number of elements in set A
The set \( A \) has 4 elements: \( 1, 2, 3, \) and \( 4 \).

### Step 2: Determine the number of elements excluding 3
If we want to find subsets that contain the element \( 3 \), we can consider the remaining elements in the set \( A \) after excluding \( 3 \). The remaining elements are \( 1, 2, \) and \( 4 \).

### Step 3: Calculate the number of subsets of the remaining elements
The number of subsets of a set with \( n \) elements is given by \( 2^n \). In this case, we have 3 remaining elements (1, 2, and 4). Therefore, the number of subsets of these 3 elements is:
\[ 2^3 = 8 \]

### Step 4: Include the element 3 in each subset
Since we want subsets that contain the element \( 3 \), we can combine the 8 subsets of the remaining elements with the element \( 3 \). Each of these subsets can be paired with \( 3 \) to form a valid subset of \( A \) that contains \( 3 \).

### Conclusion
Thus, the total number of subsets of \( A \) that contain the element \( 3 \) is \( 8 \).

### Final Answer
The number of subsets of \( A \) that contain the element \( 3 \) is \( 8 \).

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