MA121 Lecture Notes - Lecture 4: Subset, Empty Set, Contraposition
Document Summary
Fall 2018: recall the truth tables of the following most basic logical operations on simple statements p and q with connectives. Truth tables of all other compound statements involving two or more simple statements may be constructed using the above basic ones. Recall the following most frequently used nontrivial equivalence relationships: De morgan s laws p q q p p (q r) (p q) (p r) (p q) ( p) ( q) p (q r) (p q) (p r) (p q) ( p) ( q) These equivalences, together with other more trivial equivalences such as p ( p), may be used to verify other equivalence relationships. Let a, b and c be sets containing elements of the same non-empty universal set u . Recall the following de nitions and theorems from set theory. The sets a and b are equal, denoted a = b, if a and b contain exactly the same elements.
