1. (1.4) An Introduction to Logic
Logic is a tool that allows us to apply mathematical reasoning in problem solving.
Definition: A statement is a sentence that is either true or false, but not both.
Example (i): Which of the following are statements?
Definition: If p is a statement then ~p is the negation of p. Negation means making the opposite statement.

2. Example (ii): Negate each of the following statements.
Definition: There are two types of quantifiers that appear in sentences.
Universal quantifiers: all, every, no, none
Existential quantifiers: some, there exists
Statement Negation

3. Definition: There are two ways to create compound statements by using connections.
Conjunction: p Λ q means statement p AND statement q.
Disjunction: p V q means statement p OR statement q.

4. (p --> q) is equivalent to (~q --> ~p)
Contrapositive
(p --> q) is equivalent to (~q --> ~p)
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Statement: If p then q. (p --> q)
Converse: If q then p. (q --> p)
Inverse: If not p then not q. (~p --> ~q)
Contrapositive: If not q then not p. (~q --> ~p)