midterm review suckers

CL/CL*

100

The alphabet for CL

What is P and Q

200

The operators in CL*

What is a conditional

300

How do you make this an assertion? 

Go pet the Cat!

What is I love petting the cat?

(Numerous answers) 

400

What is the antecedent and consequent?

(P →(P →P)  

What is antecedent P 

What is the consequent P →P

500

What are the subformulas in this wff? 

((( P →P)  →Q) →Q) 

What are: (P→P)

(P→P)→Q)

TFL

100

What are the operators for TFL and their names, and English translation: 

&: Conjunction, and

→: conditional, then

o: disjunction, or

↔: biconditional, iff

~: negation, not

200

What is the truth table for conjunction and disjunction

Conjunction: TFFF

Disjunction: TTTF

300

What is the main connective in this wff?

~(Fa o (Ab&Jb))

What is ~

400

Explain the differences between logical falsity, logical truth, and logical contingency? 

Logical falsity: cannot ever be true

Logical truth: cannot ever be false

Logical contingency: truth values are both true and false

500

Explain the differences between logical satisfiability, entailment, and validity.

Satisfiable: an entire row is true

Entailment: every row where P is true, Q is false as well

Validity: It is impossible for the premise to be true and the conclusion false 

Models

100

What does it mean to create an extensional model?

and What does it mean to create a total, partial, and adequate model? 

Extensional: Formal, contains the domain, all extensions, and all referents.

Total, partial, and adequate model: contains only the truth values asked, domain is not needed

200

What is the difference between a term function and a predicate function? 

Term function: points to the name of each individual, represented by tau 

Predicate function: points to each predicate to the set of individuals that include the predicate, represented by a pi

300

Create an extensional, partial, and adequate model for this wff:

((Fa→Ga)→Ga)

Answers will vary

Must include domain, terms, and predicates

400

Create an extensional, partial, adequate model that makes this wff false:

((Fa→Gb) o (~Fb&Ga)

Answers Vary

500

Create an extensional, partial, adequate model with a true wff

Answers vary

Truth Tables/Constraints

100

Write down a WFF in TFL that represents this breakfast constraint (B)

You can eat sugary cereal (c) for breakfast then you cannot eat a pop tart (a) for lunch

(Bc→~Ba)

200

Create a truth table of the wff: 

~ ( Ab & Gb ) → Fh )

Only One True in the second row

300

Create a truth table of the wff, and label the semantic properties

TFFT

Satisfiable, 

Contingent, 

Valid 

400

Create a combined truth table: 

(Ab&Fc),(AboFc), ~Fc

TFFF

TTTF

FTFT

500

Create a combined truth table and label the semantic properties: 

TTFFTTT

TTFTTTFT

TFFFTFFF

Satisfiable, contingent, entails 

Disjunctive Normal Form and others

100

Is this in disjunctive normal form? 

(Gd & Fd & ∼H f)

_Nope

200

Is this in disjunctive form? 

(Fa & Gb) ◦ (Fa & Gb)

Yessir

300

Check to see if the following wff is satisfiable 

{Ha, (Id → ∼Ha), Id}

Not satisfiable 

400

Make a combined truth table to see if the wff is valid:

 {(Fa → Gb), (Gb → Hc)} |= (Fa → Hc)

Valid!

500

Convert the following to disjunctive normal form

(Gd ↔ ∼H f)

(Gd&~Af) o (~Gd&Af)