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
To find the symmetric difference A E, we can use the formula: A E = (A - E) (E - A) Given sets: E = \1, 2, 3, 4\ A = \1, 3, 5\ Step 1: Find A - E (elements in A but not in E). A - E = \x x A and x E\ A - E = \1, 3, 5\ - \1, 2, 3, 4\ The elements in A that are not in E are just 5 (since 1 and 3 are in E). A - E = \5\ Step 2: Find E - A (elements in E but not in A). E - A = \x x E and x A\ E - A = \1, 2, 3, 4\ - \1, 3, 5\ The elements in E that are not in A are 2 and 4 (since 1 and 3 are in A). E - A = \2, 4\ Step 3: Find the union of (A - E) and (E - A). A E = (A - E) (E - A) A E = \5\ \2, 4\ A E = \2, 4, 5\ Alternatively, we can use the formula: A E = (A E) - (A E) Step 1: Find A E (the union of A and E). A E = \1, 3, 5\ \1, 2, 3, 4\ A E = \1, 2, 3, 4, 5\ Step 2: Find A E (the intersection of A and E). A E = \1, 3, 5\ \1, 2, 3, 4\ A E = \1, 3\ Step 3: Find (A E) - (A E). A E = \1, 2, 3, 4, 5\ - \1, 3\ A E = \2, 4, 5\ Both methods yield the same result. Comparing this with the given options: A. \1, 2\ B. \2, 4, 5\ C. \1, 2, 3, 4, 5\ D. \1, 3\ The correct option is B. The final answer is B. \2,4,5\.