Taking `A={1,3,5,7}` and `B={2,4,6}`, draw the graphs of (i) `AxxA` (ii) `BxxA`.

Answer

To solve the problem of drawing the graphs of \( A \times A \) and \( B \times A \) for the sets \( A = \{1, 3, 5, 7\} \) and \( B = \{2, 4, 6\} \), we will follow these steps:

### Step 1: Define the Cartesian Product \( A \times A \)

The Cartesian product \( A \times A \) consists of all ordered pairs where the first element is from set \( A \) and the second element is also from set \( A \).

- Set \( A = \{1, 3, 5, 7\} \)

### Step 2: List all pairs in \( A \times A \)

We will create pairs by taking each element of \( A \) and pairing it with every element of \( A \):

1. For the first element \( 1 \):
- \( (1, 1) \)
- \( (1, 3) \)
- \( (1, 5) \)
- \( (1, 7) \)

2. For the second element \( 3 \):
- \( (3, 1) \)
- \( (3, 3) \)
- \( (3, 5) \)
- \( (3, 7) \)

3. For the third element \( 5 \):
- \( (5, 1) \)
- \( (5, 3) \)
- \( (5, 5) \)
- \( (5, 7) \)

4. For the fourth element \( 7 \):
- \( (7, 1) \)
- \( (7, 3) \)
- \( (7, 5) \)
- \( (7, 7) \)

### Step 3: Compile all pairs in \( A \times A \)

Combining all the pairs, we have:

\[ A \times A = \{(1, 1), (1, 3), (1, 5), (1, 7), (3, 1), (3, 3), (3, 5), (3, 7), (5, 1), (5, 3), (5, 5), (5, 7), (7, 1), (7, 3), (7, 5), (7, 7)\} \]

### Step 4: Define the Cartesian Product \( B \times A \)

Next, we will define the Cartesian product \( B \times A \) where:

- Set \( B = \{2, 4, 6\} \)
- Set \( A = \{1, 3, 5, 7\} \)

### Step 5: List all pairs in \( B \times A \)

We will create pairs by taking each element of \( B \) and pairing it with every element of \( A \):

1. For the first element \( 2 \):
- \( (2, 1) \)
- \( (2, 3) \)
- \( (2, 5) \)
- \( (2, 7) \)

2. For the second element \( 4 \):
- \( (4, 1) \)
- \( (4, 3) \)
- \( (4, 5) \)
- \( (4, 7) \)

3. For the third element \( 6 \):
- \( (6, 1) \)
- \( (6, 3) \)
- \( (6, 5) \)
- \( (6, 7) \)

### Step 6: Compile all pairs in \( B \times A \)

Combining all the pairs, we have:

\[ B \times A = \{(2, 1), (2, 3), (2, 5), (2, 7), (4, 1), (4, 3), (4, 5), (4, 7), (6, 1), (6, 3), (6, 5), (6, 7)\} \]

### Final Result

The graphs of the Cartesian products are as follows:

- \( A \times A = \{(1, 1), (1, 3), (1, 5), (1, 7), (3, 1), (3, 3), (3, 5), (3, 7), (5, 1), (5, 3), (5, 5), (5, 7), (7, 1), (7, 3), (7, 5), (7, 7)\} \)

- \( B \times A = \{(2, 1), (2, 3), (2, 5), (2, 7), (4, 1), (4, 3), (4, 5), (4, 7), (6, 1), (6, 3), (6, 5), (6, 7)\} \)