If A={1,2,3} and B={1,2}, then represent `AxxB` graphically.

Answer

To represent the Cartesian product \( A \times B \) graphically for the sets \( A = \{1, 2, 3\} \) and \( B = \{1, 2\} \), we will follow these steps:

### Step 1: Understand the Cartesian Product
The Cartesian product \( A \times B \) consists of all possible ordered pairs \( (a, b) \) where \( a \) is an element from set \( A \) and \( b \) is an element from set \( B \).

### Step 2: List the Elements of Each Set
- Set \( A = \{1, 2, 3\} \)
- Set \( B = \{1, 2\} \)

### Step 3: Generate Ordered Pairs
Now, we will create ordered pairs by combining each element of \( A \) with each element of \( B \):
- For \( a = 1 \):
- \( (1, 1) \)
- \( (1, 2) \)
- For \( a = 2 \):
- \( (2, 1) \)
- \( (2, 2) \)
- For \( a = 3 \):
- \( (3, 1) \)
- \( (3, 2) \)

### Step 4: List All Ordered Pairs
The complete set of ordered pairs from the Cartesian product \( A \times B \) is:
\[ A \times B = \{(1, 1), (1, 2), (2, 1), (2, 2), (3, 1), (3, 2)\} \]

### Step 5: Graphically Represent the Cartesian Product
To represent this graphically, we will draw two circles (or boxes) to represent the sets \( A \) and \( B \):

1. Draw a circle for set \( A \) and label it with its elements:
- Inside the circle, write \( 1, 2, 3 \).

2. Draw another circle for set \( B \) and label it with its elements:
- Inside the circle, write \( 1, 2 \).

3. Draw arrows (or lines) from each element in set \( A \) to each element in set \( B \):
- From \( 1 \) in \( A \) to \( 1 \) and \( 2 \) in \( B \).
- From \( 2 \) in \( A \) to \( 1 \) and \( 2 \) in \( B \).
- From \( 3 \) in \( A \) to \( 1 \) and \( 2 \) in \( B \).

### Final Representation
The graphical representation will show all elements of set \( A \) connected to all elements of set \( B \) through arrows, indicating the relationships defined by the Cartesian product.