Question

Let S = {2, 4, 6} and T = {1, 3, 5}. Use the set-roster notation to write each of the following sets, and indicate the number of elements that are in each set.

a. S x T
b. T x S
c. S x S
d. T x T

Answer 1

The sets S x T, T x S, S x S, and T x T all have 9 elements each, formed by pairing each element from the first set with every element of the second set, resulting in 3x3=9 ordered pairs for each Cartesian product.

Step-by-step explanation:

The student asked for help in writing sets in set-roster notation and determining the number of elements in each set for the following scenarios: a. S x T, b. T x S, c. S x S, and d. T x T, where S = {2, 4, 6} and T = {1, 3, 5}.

• The Cartesian product S x T is { (2, 1), (2, 3), (2, 5), (4, 1), (4, 3), (4, 5), (6, 1), (6, 3), (6, 5) } with 9 elements.
• The Cartesian product T x S is { (1, 2), (1, 4), (1, 6), (3, 2), (3, 4), (3, 6), (5, 2), (5, 4), (5, 6) } with 9 elements.
• The Cartesian product S x S is { (2, 2), (2, 4), (2, 6), (4, 2), (4, 4), (4, 6), (6, 2), (6, 4), (6, 6) } with 9 elements.
• The Cartesian product T x T is { (1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5) } with 9 elements.

Each set contains a total of 9 ordered pairs. By using the Cartesian product, we pair each element of the first set with every element of the second set, and since there are three elements in both sets S and T, we end up with 3x3=9 possible ordered pairs for each product.