These notes present the lessons I developed over the years to help beginning mathematics students to understand the logic in a proof. Professional mathematicians use these tools instinctively, often without realizing that most people have to think carefully to see how logic works. It is a brief, informal introduction to logic as it is used in construction of arguments. It provides the logic tools needed to understand a proof by contradiction, proof of the contrapositive or reductio ad absurdum.

The essential elements of predicate logic as presented here are the following.

• Predicates
• OR, AND, NOT
• IF…THEN
• Converse
• Contrapositive
• Quantifiers
• Arguments and proof

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