This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to the questions in the image: a) What is the definition of a set? A set is a collection of distinct objects, where the order of the objects does not matter. These objects are called elements or members of the set. b) List the elements of the set A = x | x is an even number between 1 and 10 The elements of set A are the even numbers that are greater than 1 and less than 10. The elements are: 2, 4, 6, 8. So, A = 2, 4, 6, 8. c) If A = 1, 2, 3, 4 and B = 3, 4, 5, 6, find A ∪ B. The union of two sets A and B, denoted by A ∪ B, is the set of all elements that are in A, or in B, or in both. A ∪ B = 1, 2, 3, 4 ∪ 3, 4, 5, 6 Combine all unique elements from both sets: A ∪ B = 1, 2, 3, 4, 5, 6 d) If A = 1, 2, 3, 4 and B = 3, 4, 5, 6, find A ∩ B. The intersection of two sets A and B, denoted by A ∩ B, is the set of all elements that are common to both A and B. A ∩ B = 1, 2, 3, 4 ∩ 3, 4, 5, 6 Identify the elements that appear in both sets: A ∩ B = 3, 4 e) If A = 1, 2, 3, 4 and B = 3, 4, 5, 6, find A - B. The difference of two sets A and B, denoted by A - B, is the set of all elements that are in A but not in B. A - B = 1, 2, 3, 4 - 3, 4, 5, 6 Remove elements from A that are also present in B: A - B = 1, 2 f) If A = 1, 2, 3, 4 and B = 3, 4, 5, 6, find B - A. The difference of two sets B and A, denoted by B - A, is the set of all elements that are in B but not in A. B - A = 3, 4, 5, 6 - 1, 2, 3, 4 Remove elements from B that are also present in A: B - A = 5, 6 Send me the next one 📸