Chapter 10

Question 1

truth functional logic

Answer 1

also known as propositional or sentential logic: prominent since the late 19th uses truth values in functions as input and produces truth values (Wikipedia)
the truth of the compound claim results entirely from the truth values of the smaller parts

Question 2

T-F

Answer 2

Truth- functional

Question 3

What do uppercase letters represent in categorical logic and what do they represent in T-F logic?

Answer 3

in categorical: terms

in T-F: claims

Question 4

claim variables

Answer 4

statements that can be true or falls, can be linked to words like “not”, “and”, “or”.

Question 5

truth-table

Answer 5

displays possible truth values

Question 6

negotiation or contradictory

Answer 6

~P. Which truth value P has, the negotiation has the other: “change the truth value from T to F or from F to T, depending on P’s values.”

Question 7

A conjunction (compound claim)

Answer 7

A conjunction is true if and only if both of the simpler claims that make it up (its conjuncts) are true. Sign: “and” (Die komische Seite will mich keine “and” Zeichen machen lassen -.-)

Question 8

Some conjunction symbol words

Answer 8

and, but, even though, while

Question 9

A disjunction (compound claim)/ disjunctive conjunction

Answer 9

A disjunction is false if and only if both of its disjuncts are false. Sign: ∨ (“wedge”) words like “or”, “either.. or”, “unless”

Question 10

conditional claim (compound claim)

Answer 10

A conditional claim is false if and only if its antecedent is true and its consequent is false: Sign: P→Q, words like “if…then…”, “provided that”

Question 11

antecedent

Answer 11

first claim in a conditional claim, e.g. the P in P→Q

Question 12

consequent

Answer 12

second claim in a conditional claim, e.g. the Q in P→Q

Question 13

the four types of truth-functional claims

Answer 13

negation, conjunction, disjunction, and conditional

Question 14

Every time we add another letter to a truth table, the number of possible combinations of T and F-

Answer 14

doubles, and so, therefore, does the number of rows

in our truth table. ( r=2^n, where r is the number of rows in the table and n is the number of letters

Question 15

Two claims are truth-functionally equivalent if they

Answer 15

have exactly the same truth table—that is, if the Ts and Fs in the column under one claim are in the same arrangement as those in the column under the other.

Question 16

What is the difference between the word “if” and the phrase “only if” in a conditional claim? What does “if and only if” mean for a compound claim?

Answer 16

“if” introduces an antecedent

“only if” a consequent

Question 17

What does “if and only if” means for a claim?

Answer 17

makes both antecedent and

consequent out of the claim it introduces. e.g. P: (P→Q)”and”(Q→P)

Question 18

the phrase”provided”/ “provided that” can introduce what kind of claim?

Answer 18

An antecendent of a conditional claim

Question 19

necessary conditions

Answer 19

the necessary condition becomes the consequent of a conditional:
e.g.: “If we have combustion (C), then we must have oxygen (O).” C→O

Question 20

sufficient conditions

Answer 20

guarantees whatever it is a sufficient condition for. Being born in the United States is a sufficient condition for U.S. citizenship—that’s all one needs to be a U.S. citizen. Sufficient conditions are expressed as the antecedents of conditional claims. We would say, “If Juan was born in the United States (B), then Juan is a U.S. citizen (C)”: B→C

Question 21

the word “if” introduces a … condition, the word “only if” introduces a … condition

Answer 21

sufficient

necessary

Question 22

Unless -> How to symbolize the claim: “Paula (P) will foreclose unless Quincy (Q) pays up.”

Answer 22

~Q→P, but better: P∨Q, because they are truth-functionally equivalent

Question 23

The word “either” in a claim symbolizes..?

Answer 23

Where a disjunction begins.
E.g: Either P and Q or R= (P & Q) v R
P and either Q or R= P& (Q v R)

Question 24

Once more please: The word “if” tells us where a … begins

Answer 24

Where a conditional claim begins
E.g: P and if Q then R= P&Q->R
If P and Q then R= (P&Q)->R

Question 25

An argument is valid, if and only if

Answer 25

the truth of the premises guarantees the truth of the conclusion—that is, if the premises were true, the conclusion could not then be false. (Where validity is concerned, remember, it doesn’t matter whether the premises are actually true.)

Question 26

The truth-table test for validity

Answer 26

Just take the claims of the argument, make the truth-table and compare with your argument if it must be right if the premises are right

Question 27

the short truth-table method underlying principle

Answer 27

If an argument is invalid, there has to be at least one row in the argument’s truth table where the premises are true and the conclusion is false. With the short truth-table method, we simply focus on finding such a row.

Question 28

"if the premises are all true in one row and so is the conclusion, the conclusion follows from the premises" right or wrong?

Answer 28

Wrong, every case of right conclusion must fit right premises, no wrong conclusion can have right premises

Question 29

deduction

Answer 29

deduce (or “derive”) the conclusion from the premises by means of a series of basic, truth-functionally valid argument patterns.

Question 30

Rule 1: Modus ponens (MP): affirming the antecedent

Answer 30

If you have a conditional among the premises, and if the antecedent of that conditional occurs as another premise, then by modus ponens the consequent of the conditional follows from those two premises. The antecedent can be just one letter or some compound claim

Question 31

annotation

Answer 31

notes about the logical steps that were made

Question 32

modus ponens rule and all other Group I rules can be used only on whole lines.

Answer 32

``` Oui E.g: (P → Q) ∨ R P _____ Q ∨ R is not a valid deduction ```

Question 33

Rule 2: Modus tollens (MT)

Answer 33

``` or denying the consequent: If you have a conditional claim as one premise and if one of your other premises is the negation of the consequent of that conditional, you can write down the negation of the conditional’s antecedent as a new line in your deduction. E.g.: P → Q ~Q _______ ~P ```

Question 34

Rule 3: Chain argument (CA)

Answer 34

``` allows you to derive a conditional from two (conditionals) you already have, provided the antecedent of one of your conditionals is the same as the consequent of the other. E.g: P → Q Q → R ______ P → R ```

Question 35

Rule 4: Disjunctive argument (DA)

Answer 35

``` From a disjunction and the negation of one disjunct, the other disjunct may be derived. E.g.: P ∨ Q ~P ____ Q ```

Question 36

Rule 5: Simplification (SIM)

Answer 36

If the conjunction is true, then of course the conjuncts must all be true. You can pull out one conjunct from any conjunction and make it the new line in your deduction. E.g: P & Q ____ P

Question 37

Rule 6: Conjunction (CONJ)

Answer 37

``` This rule allows you to put any two lines of a deduction together in the form of a conjunction. P Q ____ P & Q ```

Question 38

Rule 7: Addition (ADD)

Answer 38

no matter what claims P and Q might be, if P is true then either P or Q must be true. The truth of one disjunct is all it takes to make the whole disjunction true. P _____ P ∨ Q

Question 39

Rule 8: Constructive dilemma (CD)

Answer 39

``` The disjunction of the antecedents of any two conditionals allows the derivation of the disjunction of their consequents. P → Q R → S P ∨ R ______ Q ∨ S ```

Question 40

Rule 9: Destructive dilemma (DD)

Answer 40

``` The disjunction of the negations of the consequents of two conditionals allows the derivation of the disjunction of the negations of their antecedents. P → Q R → S ~Q ∨ ~S _______ ~P ∨ ~R ```

Question 41

The 9 group 1 rules

Answer 41

1) Modus ponens (MP), 2) Modus tollens (MT), 3) Chain argument (CA), 4) Disjunctive argument (DA), 5) Simplification (SIM), 6) Conjunction (CONJ), 7) Addition (ADD), 8) Constructive dilemma (CD) 9) Destructive dilemma (DD)