Set Operations Examples

Set Theory · Axiom Academy

Computing union, intersection, difference, and complement The universal set (U) is the set of every element under consideration in this problem — each set below is a subset of it, and a set's complement (such as Aᶜ) is everything in U that the set leaves out. Calculate the following expressions step by step: A = 1, 2, 3, 4, 5 , B = 4, 5, 6, 7, 8 , C = 2, 4, 6, 8, 10 , U = 1, 2, ..., 10 Elements in BOTH A and B: A ∩ B = 4, 5 Elements in A OR C (or both): A ∪ C = 1, 2, 3, 4, 5, 6, 8, 10 Elements in B but NOT in A: B \ A = 6, 7, 8 Elements in U but NOT in A: A c = 6, 7, 8, 9, 10 First A ∩ B = 4, 5 , then union with C: (A ∩ B) ∪ C = 2, 4, 5, 6, 8, 10 A ∩ B: Look for elements in BOTH sets A ∪ B: Combine all elements (no duplicates) A \ B: Elements in A that are NOT in B A c : Everything in U that's NOT in A Order matters: For compound expressions, work inside out (parentheses first) Check your work: Verify results make sense with set sizes

This is the written version of the interactive lesson above. See the full Set Theory course.