Logic Final Review

Question 1

T/F: If P = F and Q = F, what is the truth value of the sentence:
(Q → (P → Q))?

Answer 1

True

Question 2

T/F: If P = T and (¬P ∨ Q) = F, what is the truth value of the sentence: P → Q?

Answer 2

False

Question 3

T/F: What is the truth value on the last row of the truth table for
P → (A ∧ L)?

Answer 3

False

Question 4

T/F: An invalid argument can have true premises and a true conclusion.

Answer 4

True

Question 5

T/F: A sound argument can have true premises but a false conclusion.

Answer 5

False

Question 6

T/F: A conditional whose antecedent is a contradiction is a tautology.

Answer 6

True

Question 7

T/F: If the consequent of a conditional is a tautology then the conditional is a tautology.

Answer 7

True

Question 8

T/F: A ∨ ¬A

Answer 8

True

Question 9

T/F: A ∧ ¬A

Answer 9

False

Question 10

T/F: P → (Q ∨ ¬Q)

Answer 10

True

Question 11

T/F: (x)((Px → ¬Qx) ∨ ¬(¬Px ∨ ¬Qx))

Answer 11

True

Question 12

T/F: All WFFs in PL and SL will have twice as many disjuncts as disjunctions.

Answer 12

True

Question 13

T/F: All PL rules are valid inferences.

Answer 13

True

Question 14

T/F: No sound argument is invalid.

Answer 14

True

Question 15

T/F: Any row in an argument’s truth table having true premises and a true conclusion shows that the argument is valid.

Answer 15

False

Question 16

T/F: It takes only one invalidating row to show than an argument is invalid.

Answer 16

True

Question 17

T/F: What is the truth value of the following sentence?
(P → Q) ∨ ¬(¬P ∨ Q)

Answer 17

True

Question 18

T/F: Any argument with a tautology for its conclusion is a valid argument.

Answer 18

True

Question 19

T/F: An SL expression can be a formula and not a WFF.

Answer 19

False

Question 20

T/F: A PL expression can be a formula and not a WFF.

Answer 20

True

Question 21

English is a natural language. SL is a/an:
a. unnatural language
b. artificial language
c. natural symbolism
d. derivation system

Answer 21

b. artificial language

Question 22

SL stands for
a. symbolic language
b. sentential logic
c. symbolic logic
d. sheldon lee

Answer 22

b. sentential logic

Question 23

PL stands for
a. Predictive Language
b. Programming Language
c. Predicate Logic
d. Patti Smith

Answer 23

c. predicate logic

Question 24

Logic derives from which Greek word?
a. Logos
b. Logy
c. Scienlogical
d. Toga

Answer 24

a. logos

Question 25

You ought not to rely on the what? a. laws of probability b. the premises of an argument c. anything unreliable d. anything too reliable

Answer 25

c. anything unreliable

Question 26

If the consequent of a conditional is a contradiction then the conditional is a. a contradiction b. a tautology c. contingent d. any of the above

Answer 26

d. any of the above

Question 27

If the sufficient condition of a conditional is a contradiction then the conditional is a. a contradiction b. a tautology c. contingent d. any of the above

Answer 27

b. a tautology

Question 28

If a disjunct is a contradiction then the disjunction is a. a contradiction b. a tautology c. contingent d. any of the above

Answer 28

d. any of the above

Question 29

If the sufficient and necessary condition of a conditional are both contradictions then the conditional is a. a contradiction b. a tautology c. contingent d. any of the above

Answer 29

b. a tautology

Question 30

If a conjunct is a contradiction then the conjunction is a. a contradiction b. a tautology c. contingent d. any of the above

Answer 30

a. a conttradiction

Question 31

Contra is a. an equivalence b. an equivalence in SL but not PL c. a syllogism d. a fallacy

Answer 31

a. an equivalence

Question 32

Translate the following. If every (f)act is (T)rue then every (l)ie is a (c)ontradiction. a. (x)(Fx → Tx) ∧ (x)(Lx → Cx) b. (x)((Fx → Tx) → (Lx → Cx)) c. (x)(Fx → Tx) → (x)(Lx → Cx) d. (x)(Fx ∧ Lx) → (x)(Lx ∧ Cx)

Answer 32

a. (x)(Fx → Tx) ∧ (x)(Lx → Cx)

Question 33

What rule requires a disjunction and the negation of one of the disjuncts? a. Add b. CA c. DA d. Simp

Answer 33

c. DA

Question 34

What rule uses a conditional and the negation of the antecedent? a. MP b. MT c. DA d. There isn't one

Answer 34

d. There isn't one

Question 35

What rule requires only a conditional to arrive at a conjunction? a. MT b. Imp c. DeM d. there isn't one

Answer 35

d. there isn't one

Question 36

What kind of thing is an argument? a. a disagreement b. a question c. a sentence d. a set of sentences

Answer 36

d. a set of sentences

Question 37

Which of the following would NOT be a step in building the sentence (¬A ∧ B) ∨ C, using the recursive rules for well-formed formulas (WFFs) of SL? a. A b. ¬A c. A ∧ B d. C

Answer 37

c. A ∧ B

Question 38

Among these rules, which would be used the earliest in building the SL sentence (¬A ∧ B) ∨ C? a. R¬ b. R∧ c. R∨ d. R→

Answer 38

a. R¬

Question 39

In what two ways do we make an artificial language more precise than a natural language? a. syntax and symbols b. syntax and semantics c. true and false d. symbols and sentences

Answer 39

b. syntax and semantics

Question 40

How many rows would the truth table for the following sentence have? (P → Q) ∨ (Q ∧ P) a. 2 b. 4 c. 8 d. 12

Answer 40

b. 4

Question 41

What kind of sentence is a sentence which has no False rows in its truth table? a. contradiction b. contingent c. tautology d. valid

Answer 41

c. tautology

Question 42

The strongest form of support relation between premises and a conclusion is called what? a. Semantics b. Validity c. Soundness d. Verification

Answer 42

b. validity

Question 43

Each of our two-place connectives (and, or, if-then) has a unique condition which makes it easy to remember. What is the unique condition for "if-then"? a. Only True when both conjuncts are True b. Only False when both disjuncts are False c. Only False when the antecedent is False and the consequent is True d. Only False when the antecedent is True and the consequent is False

Answer 43

d. Only False when the antecedent is True and the consequent is False

Question 44

Which of the following is NOT a unique condition for any of our three connectives? a. only true when both conjuncts are true b. only false when both disjuncts are false c. only false when the antecedent if false and the consequent is true d. only false when the antecedent is true and the consequent is false

Answer 44

c. only false when the antecedent if false and the consequent is true

Question 45

Which of the following is true about a valid argument? a. they cannot have true premises and a true conclusion b. they cannot have false premises and a true conclusion c. they cannot have true premises and a false conclusion d. they cannot have false premises and a false conclusion e. all of the above

Answer 45

c. they cannot have true premises and a false conclusion

Question 46

Which of the following is true about a sound argument? a. they can have true premises and a true conclusion b. they can have false premises and a true conclusion c. they can have true premises and a false conclusion d. they can have false premises and a false conclusion e. all of the above

Answer 46

a. they can have true premises and a true conclusion b. they can have false premises and a true conclusion d. they can have false premises and a false conclusion

Question 47

What kind of sentence is false on every TVA? a. tautology b. contradiction c. contingent d. valid

Answer 47

b. contradiction

Question 48

What's the correct SL translation of the following sentence? I will (p)ass the course only if I (a)ce the final. a. A → P b. P → A c. (P→ A) ∧ (A → P) d. None of the above

Answer 48

b. P → A

Question 49

Contraries cannot be what together?

Answer 49

true

Question 50

A conjunction is only true when its conjuncts are both what?

Answer 50

true

Question 51

A conjunction of contraries cannot be what?

Answer 51

true

Question 52

A conditional is false if and only if the antecedent is true and the consequent is what?

Answer 52

false

Question 53

If the antecedent of a conditional is a conjunction of contraries then the conditional can never be what?

Answer 53

false

Question 54

If the consequent of a conditional is a disjunction of subcontraries then the conditional can never be what?

Answer 54

false

Question 55

If the necessary condition of a conditional is a disjunction of subcontraries then the conditional can never be what?

Answer 55

false

Question 56

A ∧ B _______________________________ (A ∧ B) ∧ C Conj

Answer 56

C

Question 57

A ∧ B ______________________________ (B ∧ C) MP

Answer 57

(A ∧ B) → (B ∧ C)

Question 58

A ∧ B ____________________________ (B ∧ C) MT

Answer 58

¬(B ∧ C) → ¬(A ∧ B)

Question 59

P → ¬P ____________________________ P → P CA

Answer 59

¬P → P

Question 60

_____________________________ P → P Imp

Answer 60

¬P ∨ P

Question 61

(∃x)Wx ________________________________ (∀x)(Wx ∨ Qx) MP

Answer 61

(∃x)Wx → (∀x)(Wx ∨ Qx)

Question 62

_____________________________ (∀x)(Mx ∨ Qx) Imp

Answer 62

(∀x)(¬Mx → Qx)

Question 63

_____________________________________ (∀x)((Mx ∧ Qx) ∨ Px) Imp

Answer 63

(∀x)(¬(Mx ∧ Qx) → Px)