Reasoning-Intermediate Logic 2/17/26

Ch 1-14 Vocab

100

a valid argument which presents a choice between two conditionals.

dilemma

200

a valid argument form which can be used to justify steps in a proof

rule of inference

300

a branch of formal, deductive logic in which the basic unit of thought is the proposition

Propositional Logic

400

a statement

proposition

500

a proposition that has only one component part

simple propostition

Logical Operators

100

p ~p

Negation

200

p     q         p = q

Biconditional

300

p  q      p  * q

Conjunction

400

p   q    p v q

Disjunction

500

p  q      p>q

Conditional

Rules of Inference A

100

p implies q 

q implies r

therefore p implies r

Hypothetical Syllogism (H.S.)

200

p implies q 

therefore p implies (p and q)

Absorption (Abs.)

300

p and q

therefore p

Simplification (Simp.)

400

p or q 

not p

therefore q

Disjunctive Syllogism (D.S.)

500

(p implies q) and (r implies s)

p or r

therefore q or s

Constructive Dilemma (C.D.)

Rules of inference B

100

p implies q

p

therefore q

Modus Ponens (M.P.)

200

p or q

not p

therefore q

Disjunctive Syllogism

300

p

q

therefore p and q

Conjunction (conj.)

400

p

therefore p or q

Addition (Add.)

500

p implies q

not q

therefore not p

Modus Tollens (M.T.)

Ch. 15-17Vocab

100

A way of deducting a conclusion from a given set of premises

Formal Proof of Validity

200

forms of equivalent statements

rules of replacement

300

Two rules of replacement

Transposition and Exportation

400

step-by-step deduction of a conclusion from a set premises

formal proof of validity

500

a valid argument form which can be used to justify steps in a proof

Rule of inference