Four ways to prove two sets A and B equal a membership table a containment proof show that A is a subset of B show that B is a subset of A set builder notation and logical equivalences Venn diagrams
Prove lhs is a subset of rhs Prove rhs is a subset of lhs
… set builder notation and logical equivalences Defn of complement Defn of intersection De Morgan law Defn of complement Defn of union
Prove using set builder and logical equivalences
A containment proof See the text book Thats a cop out if ever I saw one!
A containment proofGuilt kicks in To do a containment proof of A = B do as follows 1. Argue that an arbitrary element in A is in B i.e. that A is an improper subset of B 2. Argue that an arbitrary element in B is in A i.e. that B is an improper subset of A 3. Conclude by saying that since A is a subset of B, and vice versa then the two sets must be equal