Set multiplication, also known as the Cartesian product of sets, is a basic operation in set theory where you combine two sets to create a new set of ordered pairs.
To perform set multiplication, follow these steps:
- Identify the Sets: Start with two sets. For example, let’s consider set A = {1, 2} and set B = {x, y}.
- Form Ordered Pairs: Create ordered pairs by taking each element of the first set (A) and pairing it with each element of the second set (B). This means you will take the first element of set A and pair it with each element of set B, then move to the next element in set A.
- Compile the Resulting Pairs: From the example sets, the pairs would be as follows:
- (1, x)
- (1, y)
- (2, x)
- (2, y)
- Write the Resulting Set: The resulting set, called the Cartesian product, is denoted as A × B and consists of all the ordered pairs you have formed. In this case, A × B = {(1, x), (1, y), (2, x), (2, y)}.
Remember, the order of the sets matters. The pairs (1, x) and (x, 1) are different as the first element comes from set A and the second from set B. Practice with different sets to become comfortable with the process!