The Cartesian product A × B is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B, which is {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}.
Questions & Step-by-step Solutions
1 item
Q
Q: If A = {1, 2, 3} and B = {3, 4}, what is the Cartesian product A × B?
Solution: The Cartesian product A × B is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B, which is {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}.
Steps: 7
Step 1: Identify the sets A and B. A = {1, 2, 3} and B = {3, 4}.
Step 2: Understand that the Cartesian product A × B means we will create pairs (a, b) where 'a' is from set A and 'b' is from set B.
Step 3: Start with the first element of A, which is 1. Pair it with each element of B: (1, 3) and (1, 4).
Step 4: Move to the next element of A, which is 2. Pair it with each element of B: (2, 3) and (2, 4).
Step 5: Now take the last element of A, which is 3. Pair it with each element of B: (3, 3) and (3, 4).
Step 6: Collect all the pairs you created: {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}.
Step 7: This collection of pairs is the Cartesian product A × B.
