If `A={1,2,3,4},` then the number of subsets of set A containing element 3, is

Options

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

Answer

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

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

**Hint:** Count the elements in the set to determine how many total options you have.

### Step 2: Fix the element \( 3 \) in the subset
Since we want subsets that must contain the element \( 3 \), we will include \( 3 \) in every subset we form.

**Hint:** Remember that every subset we are interested in must have the element \( 3 \).

### Step 3: Determine the remaining elements
The remaining elements in set \( A \) after including \( 3 \) are \( 1, 2, \) and \( 4 \).

**Hint:** Identify which elements can be included or excluded in the subsets along with \( 3 \).

### Step 4: Calculate the number of combinations of the remaining elements
For each of the remaining elements \( 1, 2, \) and \( 4 \), we have two choices: either include the element in the subset or exclude it.

Since there are 3 remaining elements, the number of combinations can be calculated as:
\[ 2^{\text{number of remaining elements}} = 2^3 = 8 \]

**Hint:** Use the formula \( 2^n \) where \( n \) is the number of elements you can choose to include or exclude.

### Step 5: Conclusion
Therefore, the total number of subsets of set \( A \) that contain the element \( 3 \) is \( 8 \).

**Final Answer:** The number of subsets of set \( A \) containing the element \( 3 \) is \( 8 \).

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