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 (Assoc.)
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 Constructive Dilemma (C.D.)
This rule says that the negation of a negation of a proposition is equivalent to that proposition.
What is Double Negation (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.)
p ⊃ q
q ⊃ r
∴ p ⊃ r
What is Hypothetical Syllogism (H.S.)
This rule of inference has the following conclusion:
∴ 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 (q v 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 this proof
1) P v Q
2) ~P
3) Q ⊃ R / ∴R
4) Q
5) 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
1) ~A • B
2) C ⊃ A
3) C v D / ∴ D
4) ~A
5) ~C
6) 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's Theorems (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 always removes the second conjunct in the conjunction.
What is Simplification (Simp.)
p • q
∴ p
quod erat demonstrandum
[p • (q v r)] ≡ [(p • q) v (p • r)]
[(p v (q • r)] ≡ [(p v q) • (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"