If A`={2,-3} and B={1,3,5}`, then find `AxxB` and `BxxA`.

Answer

To solve the problem, we need to find the Cartesian products \( A \times B \) and \( B \times A \) for the given sets \( A' = \{2, -3\} \) and \( B = \{1, 3, 5\} \).

### Step 1: Define the Sets
We have:
- Set \( A = \{2, -3\} \)
- Set \( B = \{1, 3, 5\} \)

### Step 2: Find \( A \times B \)
The Cartesian product \( A \times B \) consists of all ordered pairs \( (a, b) \) where \( a \) is an element from set \( A \) and \( b \) is an element from set \( B \).

1. Take the first element from set \( A \) which is \( 2 \):
- Pair it with each element in \( B \):
- \( (2, 1) \)
- \( (2, 3) \)
- \( (2, 5) \)

2. Now take the second element from set \( A \) which is \( -3 \):
- Pair it with each element in \( B \):
- \( (-3, 1) \)
- \( (-3, 3) \)
- \( (-3, 5) \)

Combining all these pairs, we get:
\[ A \times B = \{(2, 1), (2, 3), (2, 5), (-3, 1), (-3, 3), (-3, 5)\} \]

### Step 3: Find \( B \times A \)
The Cartesian product \( B \times A \) consists of all ordered pairs \( (b, a) \) where \( b \) is an element from set \( B \) and \( a \) is an element from set \( A \).

1. Take the first element from set \( B \) which is \( 1 \):
- Pair it with each element in \( A \):
- \( (1, 2) \)
- \( (1, -3) \)

2. Now take the second element from set \( B \) which is \( 3 \):
- Pair it with each element in \( A \):
- \( (3, 2) \)
- \( (3, -3) \)

3. Finally, take the third element from set \( B \) which is \( 5 \):
- Pair it with each element in \( A \):
- \( (5, 2) \)
- \( (5, -3) \)

Combining all these pairs, we get:
\[ B \times A = \{(1, 2), (1, -3), (3, 2), (3, -3), (5, 2), (5, -3)\} \]

### Final Answer
Thus, the Cartesian products are:
\[ A \times B = \{(2, 1), (2, 3), (2, 5), (-3, 1), (-3, 3), (-3, 5)\} \]
\[ B \times A = \{(1, 2), (1, -3), (3, 2), (3, -3), (5, 2), (5, -3)\} \]