Basic Logic and Proof Techniques

This chapter presents a closer look at basic logic and proof techniques. Outside of mathematics, the word statement is used as a synonym for declarative sentence. In logic and mathematics, a statement must have a truth value. The chapter discusses one of the most important logical relations between two statements. Universally quantified statements are statements about all elements of a set, such as For any triangle, the angle measures sum to 180 degrees. Existentially quantified statements are statements about the existence of an element of a set with a certain property. The chapter gives some examples and basic exercises of some standard proof techniques such as proof by contradiction and proof by contraposition. Some exercise problems related to the concepts discussed in the chapter are also provided.