Let `A = { 1,2,3,4,5,6,7,8,9 , 10 ,1 1 , 12, } `
Write the subset of A containing:
all multiples of 4.

Answer

To find the subset of set \( A \) that contains all multiples of 4, we can follow these steps:

### Step 1: Identify the set \( A \)
The given set is:
\[ A = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 \} \]

### Step 2: Understand what multiples of 4 are
Multiples of 4 are numbers that can be expressed as \( 4n \), where \( n \) is an integer. For example, \( 4 \times 1 = 4 \), \( 4 \times 2 = 8 \), \( 4 \times 3 = 12 \), etc.

### Step 3: List the multiples of 4 from the set \( A \)
Now, we will check each element in set \( A \) to see if it is a multiple of 4:
- \( 1 \) is not a multiple of 4.
- \( 2 \) is not a multiple of 4.
- \( 3 \) is not a multiple of 4.
- \( 4 \) is a multiple of 4.
- \( 5 \) is not a multiple of 4.
- \( 6 \) is not a multiple of 4.
- \( 7 \) is not a multiple of 4.
- \( 8 \) is a multiple of 4.
- \( 9 \) is not a multiple of 4.
- \( 10 \) is not a multiple of 4.
- \( 11 \) is not a multiple of 4.
- \( 12 \) is a multiple of 4.

### Step 4: Collect the multiples of 4
From our checks, the multiples of 4 in set \( A \) are:
\[ 4, 8, 12 \]

### Step 5: Write the subset
The subset of \( A \) containing all multiples of 4 is:
\[ \{ 4, 8, 12 \} \]

### Final Answer
The subset of \( A \) containing all multiples of 4 is:
\[ \{ 4, 8, 12 \} \]

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