School

Ball State UniversityDepartment

Mathematical SciencesCourse Code

MATH 215Professor

AllStudy Guide

MidtermThis

**preview**shows half of the first page. to view the full**1 pages of the document.**Maths 215 Exam I Review Sheet

⋄READ THE BOOK. Re-read every section of the cov-

ered material.

⋄Re-do all the homework problems (don’t just look over

your old solutions).

⋄Know the following terms and symbols and how they

are used.

Statement/proposition

Free variable

Five main logical connectives

Truth tables

Logical equivalence

Converse

Contrapositive

Propositional Calculus

Tautology

Contradiction

Contingency

Proof sequence

Reversible proof sequence

Predicates

Universal quantiﬁer ∀

Existential quantiﬁer ∃

Quantiﬁed statement

Scope of a quantiﬁer

Universal negation

Existential negation

Deﬁnitions

Axioms/Postulates

Counterexample

Axiomatic system

Model

Direct proof and its structure

Proof by contrapositive and its structure

Proof by contradiction and its structure

↔

⇔

⇒

→

⋄Know by name and be able to prove the Equivalence

Rules:

Double Negation

Implication

DeMorgan’s Laws

Commutativity

Associativity

⋄Know by name and be able to prove the Inference

Rules:

Conjunction

Modus Ponens

Modus Tollens

Simpliﬁcation

Addition

⋄Be prepared for a problem like on the handout “In

Class Green Hair Taller Example.”

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