Midterm 2 Definitions

Question 1

When is a (particular) argument Deductively Valid?

Answer 1

If and only if it is an instance of a valid form.

Question 2

When is an argument FORM Deductively Valid?

Answer 2

If and only if there are no instances of that form in which all the premises are true and the conclusion false, aka it has no counterexample.

Question 3

When is a sentence a Compound Sentence?

Answer 3

If and only if it logically contains another complete sentence (simple sentence) as a component.

Question 4

When is a sentence a Simple Sentence?

Answer 4

If and only if it is not a compound sentence.

Question 5

What is a Sentential Operator?

Answer 5

An expression containing blanks such that, when the blanks are filled with complete sentences, the result is a complete sentence.

Question 6

When is a sentential operator Truth-Functional?

Answer 6

If and only if the truth or falsity of a compound sentence containing that operator is completely determined by the truth or falsity of its component sentences.

Question 7

What is a Counterexample to an argument form?

Answer 7

An instance of that form where all the premises are true and the conclusion false.

Question 8

When is a statement form a Tautology?

Answer 8

If and only if every instance of that form is true; that is, it is true in every row in its truth table.

Question 9

When is a statement form a Contradiction (or inconsistent)?

Answer 9

If and only if every instance of that form is false; that is, it is false in every row in its truth table.

Question 10

When is a statement form a Contigency?

Answer 10

If and only if some instance of that form is true and some is false; that is, it is true in at least one row in its truth table and false in at least one row in its truth table.

Question 11

Fill in the blank: Deductive Validity of an argument depends on its ____.

Answer 11

Form.

Question 12

What is the study of argument forms called?

Answer 12

Formal Logic.

Question 13

What is an Instance of a form?

Answer 13

When a form’s variables (ex: “p” and “q” in “p->q”) are replaced with sentences (ex: “cold” and “windy” in “if cold then windy”).

Question 14

Is the following sentence compound or simple: Jason Bay hit 3 homers and struck out.

Answer 14

Compound. Can be deconstructed as “JB hit 3 homers and JB struck out.” – still logically means the same thing though.

Question 15

Fill in the blanks: Compound sentences are built from _____ sentences by means of ______.

Answer 15

Component, sentential operators.

Question 16

True or False: Component sentences are simple sentences.

Answer 16

True.

Question 17

Name four common sentential operators.

Answer 17

“Either – or –.”
“– and –.”
“If –, then –.”
“— if and only if —“

Question 18

True or False: There are an infinite number of sentential operators in the English language.

Answer 18

True.

Question 19

Fill in the blank: If you want to know whether a (compound) sentence is true or not, determine the truth or falsity of the ___ sentences.

Answer 19

Component.

Question 20

Name the five Truth-Functional Sentential Operators.

Answer 20

Conjunction, disjunction, negation, conditional, and biconditional.

Question 21

What are a conjunction’s component sentences are called?

Answer 21

Conjuncts.

Question 22

What is an ampersand and what is it used for?

Answer 22

“And” or “&”
Used for conjunctions.

Question 23

What are a disjunction’s component sentences are called?

Answer 23

Disjuncts.

Question 24

What is the TFSO in this sentence: (B&F).

Answer 24

“&” or “and”
This is a conjunction.

Question 25

What is a wedge and what is it used for?

Answer 25

"Either, or" or "v" This is a disjunction.

Question 26

What is the TFSO in this sentence: (LvF).

Answer 26

"v" or "either, or" This is a disjunction.

Question 27

What are a negation's component sentences called?

Answer 27

Negated formulas.

Question 28

What is a tilde and what is it used for?

Answer 28

"Not" or "it is not the case that" or "~" It is used for negations.

Question 29

What is the TFSO in this sentence: ~W.

Answer 29

"~" or "not" or "it is not the case that" This is a negation.

Question 30

What are a conditional's component sentences called?

Answer 30

First component sentence is called the Antecedent. Second component sentence is called the Consequent.

Question 31

What is the only TFSO where order matters?

Answer 31

Conditional.

Question 32

What is an arrow and what is it used for?

Answer 32

"If, then" or "->" Used for conditionals.

Question 33

What is the TFSO in this sentence: (T->S).

Answer 33

"->" or "if, then" This is a conditional.

Question 34

Which goes first, "if" or "then"?

Answer 34

If, always.

Question 35

True or False: Consequent arrow Antecedent.

Answer 35

False, it is Antecedent arrow Consequent.

Question 36

What is a double arrow and what is it used for?

Answer 36

"<->" or "if and only if" Used for biconditionals.

Question 37

What is the TFSO in this sentence: (R<->A).

Answer 37

"<->" or "if and only if" This is a biconditional.

Question 38

Translate this sentence: The would be WET if i had STIRRED it.

Answer 38

(S -> W). "If" goes first always.

Question 39

True or False: Only if = If.

Answer 39

False, “Only if” = “then.”

Question 40

True or False: Only if = Then.

Answer 40

True!

Question 41

True or False: Only if = If and only if.

Answer 41

False.

Question 42

Translate this sentence: The dog will BITE only if PROVOKED.

Answer 42

(B -> P). Only if = then.

Question 43

Fill in the blank: "Unless" can also be "___" plus a _____.

Answer 43

"if", negation.

Question 44

Translate this sentence using a negation: W unless C.

Answer 44

(~C -> W).

Question 45

True or False: "I believe that" is a TFSO.

Answer 45

False.

Question 46

True or False: "___ because ___" is a TFSO.

Answer 46

False

Question 47

How do TFSOs differentiate from SOs?

Answer 47

With regular SOs, it is not enough to just know components to determine if the sentence is true or not. With TFSOs, it is.

Question 48

True or False: All compound sentences have TFSOs.

Answer 48

False, all compound sentences have SOs but not all of them are TFSOs.

Question 49

What is a WFF?

Answer 49

A well-formed formula (or grammatically correct sentence)

Question 50

Fill in the blank: S, L, and R are all examples of ___?

Answer 50

Sentence letters.

Question 51

Fill in the blanks: WFFs are built from ______ in _____ using the 5 _____.

Answer 51

Sentence letters, stages, sentential operators.

Question 52

What is a Major Operator?

Answer 52

The last operator added when a wff is built up in stages.

Question 53

True or False: Any sentence that uses sentence letters that are WFFs are NOT also WFFs.

Answer 53

False, they ARE also WFFs.

Question 54

How do you say a particular argument is valid/invalid?

Answer 54

"This particular argument is invalid/valid because its form is invalid/valid. Its form is invalid/valid because it has counterexamples/no counterexamples.”

Question 55

How do you say a statement form is a contradiction/tautology/contingency?

Answer 55

"Since the statement form is — in every row, it is a contradiction/tautology/contingency."

Question 56

When are two statement forms are Logically Equivalent?

Answer 56

When the columns below their major operators are identical (i.e. all T or all F), aka they agree in every row.

Question 57

How do you say a statement form is logically equivalent?

Answer 57

"The 2 statement forms are logically equivalent because their major operators agree in every row."

Question 58

Fill in the blank: If an argument p,q :. r is invalid, then (p&q) & ~r is a ____.

Answer 58

Contingency or tautology.

Question 59

Fill in the blank: If an argument p,q :. r is valid, then (p&q) & ~r is a ____.

Answer 59

Contradiction.

Question 60

Fill in the blank: If p is a contradiction, then p,q :. r is ____.

Answer 60

Valid.

Question 61

Fill in the blank: If r is a tautology, then p,q :. r is ____.

Answer 61

Valid.

Question 62

Fill in the blank: If an argument p,q :. r is valid, then (p&q) -> r is a _____.

Answer 62

Tautology.

Question 63

Fill in the blank: If an argument p,q :. r is invalid, then (p&q) -> r is a _____.

Answer 63

Contingency or contradiction.

Question 64

What part of a statement form determines if it is a contradiction/tautology/contingency?

Answer 64

The major operator.

Question 65

Fill in the blank: When testing deductive validity using truth tables, you can start with the _____ to rule out "T" rows (as they cannot be counterexamples) as a shortcut.

Answer 65

Conlusion.

Question 66

Fill in the blanks: (I v W) is a ____ and (p v q) is a ______.

Answer 66

Instance, form.

Question 67

True or False: Each row in a truth table is a possible world.

Answer 67

True.

Question 68

Recite the Conditional Truth Table.

Answer 68

T, T = T T, F = F F, T = T F, F = T

Question 69

Recite the Biconditional Truth Table.

Answer 69

T, T = T T, F = F F, T = F F, F = T

Question 70

Recite the Conjunction Truth Table.

Answer 70

T, T = T T, F = F F, T = F F, F = F

Question 71

True or False: (B & O) is an instance of (p & q).

Answer 71

True. Note that for a sentence to be an instance of a form it must have the same MO.

Question 72

Recite the Negation Truth Table.

Answer 72

T = F F = T

Question 73

Recite the Disjunction Truth Table.

Answer 73

T, T = T T, F = T F, T = T F, F = F

Question 74

What is the hint for Conjunction Truth Tables?

Answer 74

True if both conjuncts are true, false otherwise.

Question 75

What is the hint for Negation Truth Tables?

Answer 75

Flip-flop, opposites. If p=true, ~p=false and vice versa.

Question 76

What is the hint for Disjunction Truth Tables?

Answer 76

If its both or one or the other, then its true. If its neither, its false.

Question 77

What is the hint for Conditional Truth Tables?

Answer 77

No counterexamples, aka TF is only false.

Question 78

What is the hint for Biconditionals Truth Tables?

Answer 78

Same truth value on both sides of <-> means its true.

Question 79

Why do logicians only care about the part of the sentences that represent the conditions under which they are true/false?

Answer 79

Because they give meaning to the sentential operators.

Question 80

Translate "q if p."

Answer 80

p -> q.

Question 81

Can "q if p" be translated as q -> p?

Answer 81

No, it must be p -> q because "if" always goes first.

Question 82

True or False: "Unless" can be translated to "either, or."

Answer 82

True.

Question 83

Rewrite "p unless q."

Answer 83

(Either) p or q.

Question 84

Rewrite "unless p, q."

Answer 84

(Either) p or q.

Question 85

Which one is "only if"? 1) (p <-> q) 2) (p -> q)

Answer 85

#2. #1 is "if and only if."

Question 86

True or False: "Only if" = "then."

Answer 86

True.

Question 87

Rewrite and translate "p only if q."

Answer 87

"if p then q" (p -> q)

Question 88

Rewrite and translate "only if p, q."

Answer 88

"p, if q" or “if q then p” (q -> p)

Question 89

True or false: "Neither, nor" = "not either, or."

Answer 89

True.

Question 90

What are the two ways to translate "neither p nor q" ?

Answer 90

~(p v q) and (~p & ~q)

Question 91

True or False: "Neither p nor q" can be translated as (~p v ~q) or ~(p & q).

Answer 91

False, these are translations for "not both" which is different from "neither, nor."

Question 92

Fill in the blanks: When translating "not both," use ____ or ____.

Answer 92

Negation, disjunction.

Question 93

What are the two translations of "not both p and q" ?

Answer 93

~(p & q) and (~p v ~q)

Question 94

True or False: "Not both" can be translated as ~(p v q) and (~p & ~q).

Answer 94

False, those are translations for "neither, nor" which is different.

Question 95

Fill in the blank: Use the sentence's _____ to point you towards the major operator.

Answer 95

Commas.