If `AxxB={(a,3),(a,5),(b,3),(b,5),(c,3),(c,5)}`, then find `BxxA`.

Answer

To find \( B \times A \) given \( A \times B = \{(a, 3), (a, 5), (b, 3), (b, 5), (c, 3), (c, 5)\} \), we will follow these steps:

### Step 1: Identify the sets A and B
From the ordered pairs in \( A \times B \), we can identify the elements of sets \( A \) and \( B \):
- The first elements of the pairs represent the elements of set \( A \).
- The second elements of the pairs represent the elements of set \( B \).

From the pairs:
- Set \( A = \{a, b, c\} \)
- Set \( B = \{3, 5\} \)

### Step 2: Define the Cartesian product \( B \times A \)
The Cartesian product \( B \times A \) consists of all ordered pairs where the first element is from set \( B \) and the second element is from set \( A \). Thus, we will form pairs using each element of \( B \) with each element of \( A \).

### Step 3: Create the ordered pairs for \( B \times A \)
We will create the pairs as follows:
- For the first element \( 3 \) from \( B \):
- Pair with \( a \): \( (3, a) \)
- Pair with \( b \): \( (3, b) \)
- Pair with \( c \): \( (3, c) \)

- For the second element \( 5 \) from \( B \):
- Pair with \( a \): \( (5, a) \)
- Pair with \( b \): \( (5, b) \)
- Pair with \( c \): \( (5, c) \)

### Step 4: List all the pairs
Combining all the pairs we formed, we get:
\[ B \times A = \{(3, a), (3, b), (3, c), (5, a), (5, b), (5, c)\} \]

### Final Answer
Thus, the Cartesian product \( B \times A \) is:
\[ B \times A = \{(3, a), (3, b), (3, c), (5, a), (5, b), (5, c)\} \]

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