If A = {1, 2, 3} and B = {3, 4}, what is the Cartesian product A × B?

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Question: If A = {1, 2, 3} and B = {3, 4}, what is the Cartesian product A × B?

Options:

Correct Answer: {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}

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)}.

If A = {1, 2, 3} and B = {3, 4}, what is the Cartesian product A × B?

If A = {1, 2, 3} and B = {3, 4}, what is the Cartesian product A × B?

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.

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