If A = {1, 2, 3} and B = {1, 2, 3}, what is A × B?

If A = {1, 2, 3} and B = {1, 2, 3}, what is A × B?

Step 1: Understand what A and B are. A is the set {1, 2, 3} and B is also the set {1, 2, 3}.
Step 2: Know that A × B means we are going to pair every element in A with every element in B.
Step 3: Start with the first element of A, which is 1. Pair it with each element in B: (1,1), (1,2), (1,3).
Step 4: Move to the second element of A, which is 2. Pair it with each element in B: (2,1), (2,2), (2,3).
Step 5: Finally, take the third element of A, which is 3. Pair it with each element in B: (3,1), (3,2), (3,3).
Step 6: Collect all the pairs you created: {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}.
Step 7: This collection of pairs is the Cartesian product A × B.

Cartesian Product – The Cartesian product of two sets A and B is the set of all ordered pairs (a, b) where a is in A and b is in B.