If A = {1, 2} and B = {x | x is an odd integer}, what is A × B?
Practice Questions
1 question
Q1
If A = {1, 2} and B = {x | x is an odd integer}, what is A × B?
{(1, 1), (2, 1)}
{(1, 3), (2, 3)}
{(1, 1), (1, 3), (2, 1), (2, 3)}
{(1, 2), (2, 2)}
The Cartesian product A × B consists of all ordered pairs (a, b) where a ∈ A and b ∈ B. Thus, A × B = {(1, x), (2, x)} for all odd integers x.
Questions & Step-by-step Solutions
1 item
Q
Q: If A = {1, 2} and B = {x | x is an odd integer}, what is A × B?
Solution: The Cartesian product A × B consists of all ordered pairs (a, b) where a ∈ A and b ∈ B. Thus, A × B = {(1, x), (2, x)} for all odd integers x.
Steps: 7
Step 1: Understand what A and B are. A is the set {1, 2} and B is the set of all odd integers.
Step 2: Recall what the Cartesian product A × B means. It means we will create pairs (a, b) where 'a' is from set A and 'b' is from set B.
Step 3: Identify the elements in set A. The elements are 1 and 2.
Step 4: Identify the elements in set B. B includes all odd integers like ..., -3, -1, 1, 3, 5, ...
Step 5: Create ordered pairs using each element from A with each element from B. For each 'a' in A, pair it with 'b' in B.
Step 6: Write the pairs. For a = 1, we get (1, x) for all odd integers x. For a = 2, we get (2, x) for all odd integers x.
Step 7: Combine the pairs. The final result is A × B = {(1, x), (2, x)} for all odd integers x.
