If A = {1, 2, 3} and B = {1, 2}, what is the number of elements in A × B?

If A = {1, 2, 3} and B = {1, 2}, what is the number of elements in A × B?

Step 1: Identify the sets A and B. A = {1, 2, 3} and B = {1, 2}.
Step 2: Count the number of elements in set A. There are 3 elements in A.
Step 3: Count the number of elements in set B. There are 2 elements in B.
Step 4: Use the formula for the Cartesian product. The number of elements in A × B is the product of the number of elements in A and B.
Step 5: Calculate the product. Multiply the number of elements in A (3) by the number of elements in B (2).
Step 6: Write down the result. 3 * 2 = 6, so there are 6 elements in A × B.

Cartesian Product – The Cartesian product of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a is in A and b is in B.
Counting Elements – The number of elements in the Cartesian product is calculated by multiplying the number of elements in each set.