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
Step 1: Understand the definition of symmetric difference. The symmetric difference of two sets A and B, denoted as A B, is the set of elements that are in either A or B, but not in their intersection. It can be calculated using the formula: A B = (A - B) (B - A) or equivalently: A B = (A B) - (A B) Step 2: Identify the given sets. Given: A = \1, 2, 3\ B = \3, 4, 5\ Step 3: Calculate A - B. A - B contains elements that are in A but not in B. A - B = \1, 2, 3\ - \3, 4, 5\ = \1, 2\ Step 4: Calculate B - A. B - A contains elements that are in B but not in A. B - A = \3, 4, 5\ - \1, 2, 3\ = \4, 5\ Step 5: Calculate the union of (A - B) and (B - A). A B = (A - B) (B - A) A B = \1, 2\ \4, 5\ A B = \1, 2, 4, 5\ The symmetric difference between A and B is \1, 2, 4, 5\.