First Course in Mathematical Logic
In modern mathematics, both the theory of proof and the derivation of theorems from axioms bear an unquestioned importance. The necessary skills behind these methods, however, are frequently underdeveloped. This book counters that neglect with a rigorous introduction that is simple enough in presentation and context to permit relatively easy comprehension. It comprises the sentential theory of inference, inference with universal quantifiers, and applications of the theory of inference developed to the elementary theory of commutative groups. Throughout the book, the authors emphasize the pervasive and important problem of translating English sentences into logical or mathematical symbolism. Their clear and coherent style of writing ensures that this work may be used by students in a wide range of ages and abilities.
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TRUTH AND VALIDITY
TERMS PREDICATES AND UNIVERSAL QUANTIFIERS
UNIVERSAL SPECIFICATION AND LAWS OF IDENTITY
A SIMPLE MATHEMATICAL SYSTEM AXIOMS FOR ADDITION
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antecedent apply Associative Axiom atomic formulas atomic sentences Axiom biconditional common nouns Commutative Laws conditional proof conditional sentence conjunction Disjunctive Syllogism Double Negation English sentences equal equivalent example EXERCISE F F F F T F false and Q false sentence following arguments following sentences following sets formal proof given premises Hypothetical Syllogism identity indirect proof INTRODUCTION invalid Jane John logical symbols major connective Mary mathematical sentences means modus ponendo ponens molecular sentence negative number parentheses positive number predicate premises are true problems Prove Q is false Q is true Q V R rule of inference sentential connective set of premises step Symbolize the following symbolized sentences tautological implication tautology tell THEOREM theory Translate true and Q true or false true sentence truth assignment truth or falsity truth table truth values universal quantifier universal specification variables word write