If `A={1,3,5,7)` and `B={2,4,6}`, find `BxxB`

Answer

To find the Cartesian product \( B \times B \) where \( B = \{2, 4, 6\} \), we will follow these steps:

### Step 1: Understand the Cartesian Product
The Cartesian product \( B \times B \) consists of all possible ordered pairs \( (b_1, b_2) \) where \( b_1 \) and \( b_2 \) are elements from set \( B \).

### Step 2: List the Elements of Set B
The elements of set \( B \) are:
- \( 2 \)
- \( 4 \)
- \( 6 \)

### Step 3: Create Ordered Pairs
Now, we will create ordered pairs by pairing each element of \( B \) with every element of \( B \):
1. Pair \( 2 \) with every element in \( B \):
- \( (2, 2) \)
- \( (2, 4) \)
- \( (2, 6) \)

2. Pair \( 4 \) with every element in \( B \):
- \( (4, 2) \)
- \( (4, 4) \)
- \( (4, 6) \)

3. Pair \( 6 \) with every element in \( B \):
- \( (6, 2) \)
- \( (6, 4) \)
- \( (6, 6) \)

### Step 4: Compile the Ordered Pairs
Now, we will compile all the ordered pairs we have created:
- \( (2, 2) \)
- \( (2, 4) \)
- \( (2, 6) \)
- \( (4, 2) \)
- \( (4, 4) \)
- \( (4, 6) \)
- \( (6, 2) \)
- \( (6, 4) \)
- \( (6, 6) \)

### Step 5: Write the Result
The Cartesian product \( B \times B \) is:
\[ B \times B = \{(2, 2), (2, 4), (2, 6), (4, 2), (4, 4), (4, 6), (6, 2), (6, 4), (6, 6)\} \]