Operations on set

Introduction to Operations on Sets

Sets are a fundamental concept in mathematics. An operation on sets is a rule that combines two or more sets to create a new set. There are several operations that can be performed on sets, including:

• Union: The union of two sets A and B is the set of all elements that are in A, or in B, or in both.
• Intersection: The intersection of two sets A and B is the set of all elements that are in both A and B.
• Difference: The difference of two sets A and B is the set of all elements that are in A but not in B.
• Complement: The complement of a set A with respect to a universe set U is the set of all elements in U that are not in A.
• Cartesian product: The Cartesian product of two sets A and B is the set of all ordered pairs (a,b) where a is in A and b is in B.

Here are some examples of how these operations work:

Operation	Example	Result
Union	A = {1, 2, 3}, B = {3, 4, 5}	A ∪ B = {1, 2, 3, 4, 5}
Intersection	A = {1, 2, 3}, B = {3, 4, 5}	A ∩ B = {3}
Difference	A = {1, 2, 3}, B = {3, 4, 5}	A - B = {1, 2}
Complement	A = {1, 2, 3}, U = {1, 2, 3, 4, 5}	A' = {4, 5}
Cartesian product	A = {1, 2}, B = {3, 4}	A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}

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To better understand these operations, it's important to practice with some exercises. Here is a worksheet with examples:

Worksheet

1. Let A = {1, 2, 3} and B = {2, 3, 4}. Find A ∪ B.
2. Let A = {1, 2, 3} and B = {2, 3, 4}. Find A ∩ B.
3. Let A = {1, 2, 3} and B = {2, 3, 4}. Find A - B.
4. Let A = {1, 2, 3} and U = {1, 2, 3, 4, 5}. Find A'.
5. Let A = {1, 2} and B = {3, 4}. Find A × B.

Answers

1. A ∪ B = {1, 2, 3, 4}
2. A ∩ B = {2, 3}
3. A - B = {1}
4. A' = {4, 5}
5. A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}