Let A and B are two sets such that `A xx B` consists of 6 elements. If three elements of `A xx B = {(1, 2), (2, 3), (4, 3)}` then the remaining order pairs of `A xx B` are

Options

A. (1, 3), (2, 2), (4, 2)
B. (3, 1), (2, 2), (4, 2)
C. (3, 1), (2, 4), (2, 2)
D. (1, 3), (2, 2), (2, 4)

Answer

To solve the problem, we need to find the remaining ordered pairs in the Cartesian product \( A \times B \) given that it consists of 6 elements and 3 of those elements are already provided.

### Step-by-Step Solution:

1. **Identify the Given Ordered Pairs**:
We are given the ordered pairs:
\[ (1, 2), (2, 3), (4, 3) \]
This means we have 3 elements already in \( A \times B \).

2. **Determine the Elements of Sets A and B**:
From the given ordered pairs, we can identify the elements of sets \( A \) and \( B \):
- From \( (1, 2) \): \( 1 \in A \) and \( 2 \in B \)
- From \( (2, 3) \): \( 2 \in A \) and \( 3 \in B \)
- From \( (4, 3) \): \( 4 \in A \) and \( 3 \in B \)

Thus, we can deduce:
\[ A = \{1, 2, 4\}, \quad B = \{2, 3\} \]

3. **Count the Elements in Sets A and B**:
- The number of elements in \( A \) is 3.
- The number of elements in \( B \) is 2.

4. **Calculate the Total Number of Ordered Pairs**:
The total number of ordered pairs in \( A \times B \) is given by:
\[ |A| \times |B| = 3 \times 2 = 6 \]
This confirms that our sets are correct.

5. **List All Possible Ordered Pairs**:
The complete set of ordered pairs in \( A \times B \) can be generated as follows:
- For \( 1 \in A \): \( (1, 2), (1, 3) \)
- For \( 2 \in A \): \( (2, 2), (2, 3) \)
- For \( 4 \in A \): \( (4, 2), (4, 3) \)

Thus, the complete set of ordered pairs is:
\[ (1, 2), (1, 3), (2, 2), (2, 3), (4, 2), (4, 3) \]

6. **Identify the Remaining Ordered Pairs**:
We already have the pairs \( (1, 2), (2, 3), (4, 3) \). The remaining pairs from our complete list are:
\[ (1, 3), (2, 2), (4, 2) \]

### Final Answer:
The remaining ordered pairs of \( A \times B \) are:
\[ (1, 3), (2, 2), (4, 2) \]