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2 Be Logical

INTERMEDIATE logic Lessons 13-15

QuestionAnswer
formal proof of validity a step-by-step deduction of a conclusion from a set or premises, each step being justified by an appropriate basic rule
Formal proofs can only prove VALIDTY; they cannot prove INVALIDITY.
rule of inference a valid argument form which can be used to justify steps in a proof
modus ponens (MP) If p then q; p; therefore q
modus tollens (MT) if p then q; not q; therefore not p
hypothetical syllogism (HS) if p then q; if q then r; therefore if p then r
disjunctive syllogism (DS) p or q; not p; therefore q
constructive dilemma (CD) Both (if p then q) and (if r then s); p v r; therefore q v s
conjunction (Conj) p; q; therefore p and q
absorption (Abs) if p then q; therefore if p then (p and q)
simplification (Simp) p and q; therefore p
addition (Add) p; therefore p v q
Compound propositions of the form "not (p and q) do NOT simplify to not p.
You may NOT skip or combine steps in a proof, even if it seems obvious. You MUST explicitly perform each step AND provide justification for it.
The variables in the rules of inference can represent very complicated compound propositions.
In a proof, different variables in a rule of inference can represent the same or similar propositions.
The variables in the rules of inference may represent different propositions from ONE STEP to the NEXT STEP. That is why they are called variables.
Start a proof by comparing the conclusion with the premises.
Try saying the premises OUT LOUD or in your head to help you recognize which rules of inference to use.
Know ALL of the rules well, but especially learn how to use ABSORPTION and ADDITION.
Created by: MrsHough
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