If A = {1, 2} and B = {x | x is an odd integer}, what is A × B?

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Question: If A = {1, 2} and B = {x | x is an odd integer}, what is A × B?

Options:

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

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.

If A = {1, 2} and B = {x | x is an odd integer}, what is A × B?

If A = {1, 2} and B = {x | x is an odd integer}, what is A × B?

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.

Cartesian Product – The Cartesian product of two sets A and B is the set of all ordered pairs (a, b) where a is an element of A and b is an element of B.
Set Notation – Understanding how to interpret and work with set notation, including defining sets and elements.
Odd Integers – Recognizing the set of odd integers and how they can be represented in set notation.