That looks fine to me.nicnicman said:Homework Statement
Let A = {1, 2}, B = {3, 4}, C = {3}
What is (A x B) - (B x C)?
Homework Equations
The Attempt at a Solution
(A x B) - (B x C) = {(1, 3), (1, 4), (2, 3), (2, 4)} - {(3, 3), (4, 3)}
= {(1, 3), (1, 4), (2, 3), (2, 4)}
Since there where no elements in (B x C) that matched any elements in (A x B), I just kept the final answer equal to (A x B).
Would this be the correct way to do this?
A cartesian product is a mathematical operation that produces a set of all possible ordered pairs from two given sets. It is written as A x B, where A and B are the two sets being multiplied.
To subtract cartesian products, you first need to understand that the result of subtracting two cartesian products is another cartesian product. To find the difference, you can use the formula (A x B) - (C x D) = (A - C) x (B - D), where A and C are the first sets and B and D are the second sets. This means that you will subtract each element in C from A and each element in D from B.
Subtracting cartesian products is useful in solving problems involving sets and relations. It allows us to find the difference between two sets and can be used to determine if two sets are equal or not.
Subtracting cartesian products is a fundamental operation in set theory. It is used to find the difference between two sets, which is an important concept in set theory. It also helps in understanding the concept of subsets and complements.
Yes, for example, if we have two sets A = {1, 2, 3} and B = {3, 4, 5}, then A x B = {(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 3), (3, 4), (3, 5)}. If we want to subtract the cartesian product (2, 3) from A x B, then the result would be (A - {2}) x (B - {3}) = {(1, 4), (1, 5), (2, 4), (2, 5), (3, 4), (3, 5)}.