The PROOF is in the Pudding

Inference Schminference

Let's Jump to Conclusions

Can I Get a Replacement Over Here?

Define Your Terms

100

Identify the rule of replacement used:

[(B v C) v D] ≡ [B v (C v D)]

What is Association (Assoc.)

100

This rule combines two propositions with a conjunction

What is Conjunction (Conj.)

100

This rule of inference has the following conclusion:

∴ q v s

What is Constructive Dilemma (C.D.)

100

This rule says that the negation of a negation of a proposition is equivalent to that proposition.

What is Double Negation (D.N)

100

This is a step-by-step deduction of a conclusion from its premises

What is a formal proof of validity

200

Identify the rule of replacement used:

(F ⊃ G) ≡ (~G ⊃ ~F)

What is Transposition (Trans.)

200

p ⊃ q

q ⊃ r

∴ p ⊃ r

What is Hypothetical Syllogism (H.S.)

200

This rule of inference has the following conclusion:

∴ p ⊃ (p • q)

What is Absorption (Abs.)

200

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)]

200

This is what Q.E.D. means in English

What is "what was to be demonstrated"

300

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

300

This rule introduces a variable "out of thin air."

What is Addition (Add.)

p

∴ p v q

300

This rule of inference has the following conclusion:

∴ ~p

What is Modus Tollens (M.T)

300

This rule allows us to switch between the conditional and the disjunction when necessary.

(p ⊃ q) ≡ (~p v q)

What is Material Implication

300

These say that certain propositions are equivalent to other propositions and may replace them wherever they occur

What are the rules of replacement

400

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

400

p ⊃ q

p

∴q

What is Modus Ponens (M.P.)

400

When working out a proof, start by comparing the conclusion with the ____________

What is premises

400

This rule is named after an English logician who lived from 1806-1871

What is De Morgan's Theorems (De M.)

400

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

What is a rule of inference

500

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

500

This rule always removes the second conjunct in the conjunction.

What is Simplification (Simp.)

p • q

∴ p

500

Always conclude a proof with Q.E.D, which is Latin for __________ ____________ ___________

quod erat demonstrandum

500

[p • (q v r)] ≡ [(p • q) v (p • r)]

[(p v (q • r)] ≡ [(p v q) • (p v r)]

What is Distribution (Dist.)

500

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"

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