The PROOF is in the Pudding
Identify the rule of replacement used:
[(B v C) v D] ☰[B v (C v D)]
What is Association (Assosc.)
This rule combines two propositions with a conjunction
What is Conjunction (Conj.)
This rule of inference has the following conclusion:
∴ q v s
What is ConstructiveDilemma (C.D.)
This rule says that the negation of a negation of a proposition is equivalent to that proposition.
What is DoubleNegation (D.N)
This is a step-by-step deduction of a conclusion from its premises
What is a formal proof of validity
Identify the rule of Replacement used:
(F ⊃ G) ☰ (~G ⊃ ~F)
What is Transposition (Trans.)
What is this?
p ⊃ q
q ⊃ r
∴ p ⊃ r
What is HypotheticalSyllogism (H.S.)
This rule of inferencehas the followingconclusion:
∴ p ⊃ (p • q)
What is Absorption(Abs.)
This rule basically allows us to move parentheses around whenever the logical operators are either both disjunction or conjunction
What is Association(Assoc.)
[(p v q) v r] ≡ [p v (qv r)]
[(p • q) • r] ≡ [p • (q• r)]
This is what Q.E.D.means in English
What is "what was to be demonstrated"
Give the justification for each step in the proof:
P v Q
~P
Q ⊃ R / ∴ R
Q
R
What is
4) 1, 2 DS
5) 3, 4 MP
This rule introduces a variable "out of thin air"
What is Addition(Add.)
p
∴ p v q
This rule of inference has the following conclusion:
∴ ~p
What is Modus Tollens(M.T)
This rule allows us to switch between the conditional and the disjunction when necessary.
(p ⊃ q) ≡ (~p v q)
What is Material Implication
These say that certain propositions are equivalent to other propositions and may replace them wherever they occur
What are the rules ofreplacement
Give the justification for each step in the proof:
~A ・B
C ⊃ A
C v D / ∴ D
~A
~C
D
What is
4) 1 Simp
5) 2, 4 MT
6) 3, 5 DS
p ⊃ q
p
∴q
What is Modus Ponens (M.P.)
When working out a proof, start by comparing the conclusion with the ____________.
What is premises
This rule is named after an English logician who lived from 1806-1871
What is De Morgan'sTheorems (De M.)
A valid argument form which can be used to justify steps in a proof
What is a rule of inference
Construct a formal proof in the number of steps given:
1) A • B / ∴ A v B
2)
3)What is:
2) A 1 Simp
3) A v B 2 Add
This rule alwaysremoves the secondconjunct in theconjunction.
What is Simplification(Simp.)
p • q
∴ p
Always conclude a proof with Q.E.D, which is Latin for
quod erat demonstrandum
[p • (q v r)] ≡ [(p •q) v (p • r)]
[(p v (q • r)] ≡ [(p vq) • (p v r)]
What is Distribution (Dist.)
This is the major difference between rules of inference and rules of replacement
What is "the rules of replacement, unlike the rules of inference, allow equivalent propositions to replace each other wherever they occur, even if it is the middle of a larger proposition"