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

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

Options:

  1. {(1,1), (2,2), (3,3)}
  2. {(1,2), (2,3), (3,1)}
  3. {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}
  4. {}

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

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.

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

Practice Questions

Q1
If A = {1, 2, 3} and B = {1, 2, 3}, what is A × B?
  1. {(1,1), (2,2), (3,3)}
  2. {(1,2), (2,3), (3,1)}
  3. {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}
  4. {}

Questions & Step-by-Step Solutions

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.
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