Impossible Logic Jeopardy

Vocab

100

A diagram that shows a set of propositions being decomposed into their literals.

a Truth Tree

200

A path on a truth tree for which a contradiction has been found. 

Closed Branch

300

A path on a truth tree which includes no contradictions.

Open branch

400

Simple propositions or the negation of simple propositions.

Literals

500

This phrase means to determine the truth values of the simple propositions for which the propositions in the set would all be true.

Recover the truth values

Rules of Replacement/Inference

100

p ⊃ q
p
∴ q

Modus Ponens

200

p ⊃ q
q ⊃ r
∴ p ⊃ r

Hypothetical Syllogism

300

p ∨ q
~p
∴ q

Disjunctive Syllogism

400

(p ⊃ q) = (~q ⊃ p)

Material Implication (Implication)

500

~(p & q) = (~p v ~q)
~(p v q) = (~q & ~p)

De Morgan's Theorems

The Dungeon of Problem Solving

100

Justify each step:

1) P ⊃ Q

2) R ⊃ ~Q / ∴ P ⊃ ~R

3) ~~Q ⊃ ~R

4) Q ⊃ ~R

5) P ⊃ ~R 

2 Trans.

3 D.N.

1, 4 H.S.

200

Justify each step

1) P ⊃ ~Q / ∴ ~Q v (Q & ~P)

2) ~~Q ⊃ ~P

3) Q ⊃ ~P

4) Q ⊃ (Q & ~P) 

5) ~Q v (Q & ~P)

1 Trans

2 D.N.

3 Abs.

4 Impl.

300

Determine the validity of this argument

 (p ⊃ q)  &  [(p & q) ⊃ r]        p ⊃ (r ⊃ s)        ∴ p ⊃ s 

Valid

400

Determine the validity of this argument

 p ⊃ (q ⊃ r)        q ⊃ (p ⊃ r)        ∴ (p v q) ⊃ r

Valid

Techniques for Constructing Truth Trees

100

How many techniques in lesson 24 are there?

Four!!

200

What is the third technique for constructing truth trees?

Stop when the truth tree answers the question being asked.

300

This technique will keep you from unnecessarily rewriting propositions.

Decompose non-branching members first

400

Using this technique will help you simplify your truth tree, because it allowed you to close branches sooner.

Decompose members which result in the closing of one or more branches.

500

This technique should only be used when the other rules don't apply...

Decompose more complex propositions first.