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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?
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Practice Questions
1 question
Q1
If A = {1, 2, 3} and B = {1, 2, 3}, what is A × B?
{(1,1), (2,2), (3,3)}
{(1,2), (2,3), (3,1)}
{(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}
{}
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A × B = {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)} as it is the Cartesian product of A and B.
Questions & Step-by-step Solutions
1 item
Q
Q: If A = {1, 2, 3} and B = {1, 2, 3}, what is A × B?
Solution:
A × B = {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)} as it is the Cartesian product of A and B.
Steps: 7
Show Steps
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.
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