Logic Final (Quizzes 4 & 5)

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These statements are: R ⊃ (M ∨ ∼ C) / (P ∨ U) ⊃ C / M ⊃ ∼ P / R ≡ U

Consistent

This argument is: Q ⊃ (N ∨ S) / N ⊃ (L ⊃ B) / (S ∨ E) ⊃ (Q ⊃ B) / Q ≡ ∼ B

Consistent

Given the statement: (F ∨ ∼ S) ⊃ ∼(S ∨ ∼F)

Contingent

Statement 1A is: (N ⊃ K) ≡ (K ⊃ N)

Contingent

Statement 2C is: [G ⊃ (R • N)] ∨ [R ⊃ (G • N)]

Contingent

These statements are: J ≡ ∼ M and (J • M) ∨ ∼(M ∨ J)

Contradictory

This argument is: W∨∼ S / E ∨ ∼A / (K ∨ L) ≡ (A • S) // L ⊃ (E • W)

Valid

Given the following premises: G • ˜A K ⊃ (G • ˜A) G ⊃ M

Com

Given the following premises: 1. (G ⊃ A) ∨ T 2. G 3. ∼T

Conj

Given the following premises: 1. Q ⊃ (H • L) 2. H ⊃ ∼Q 3. L ⊃ ∼Q

Conj

The truth table for Statement 1C has how many lines? (H ∨ ∼ K) ≡ (K ⊃ H)

Four

This argument is: K ∨ E / E ⊃ ∼ K // K ≡ ∼ E

Valid

p ⊃ q q ------- p

affirming the consequent (AC) invalid

.

.

Given the following premises: 1. (F • ∼M) ⊃ (L • ∼G) 2. P ⊃ L 3. ∼(L • ∼G)

1, 3, MT

1. S ∨ (∼Q ∨ ∼C) 2. (∼Q ∨ ∼C) ⊃ M 3. T ⊃ (Q • C)

1, Assoc

A if and only if B

A ≡ B

A only if B

A ⊃ B

A if B

B ⊃ A

1. A 2. (A ⊃ ∼T) ⊃ ∼G 3. Q ⊃ (A ⊃ ∼T)

HS

Given the following premises: 1. C ⊃ (H • M) 2. (T ⊃ S) ⊃ C 3. T

HS

In Proposition 1B, the main operator is:

Horsehoe

Given the following premises: 1. A 2. G ⊃ (A ⊃ ∼L) 3. ∼A ∨ ∼G

Trans

• (Dot)

and, also, moreover, but, however, yet, still, although, nevertheless (conjunction)

Given the pair of statements: Q ≡ N and (N • ∼ Q) ∨ (Q • ∼ N)

contradictory

p ⊃ q ∼p ------- ∼q

denying the antecedent (DA) invalid

Seabourn revises its menu given that Norwegian and Princess halt tipping, unless Oceania enlarges its fleet if and only if both Costa improves its gym facilities and Regent enlarges its casinos.

[(N • P) ⊃ S] ∨ [O ≡ (C • R)]

If Heineken's being balanced implies that either Sierra is hearty or Alaskan is not sweet, then Miller's being zesty is a sufficient and necessary condition for Coors's being smooth.

[H ⊃ (S ∨ ∼A)] ⊃ (M ≡ C)

Regent's enlarging its casinos is a necessary condition for Disney's offering games if and only if Windstar's diversifying its activities is a sufficient condition for Costa's enlarging its nightspots.

(D ⊃ R) ≡ (W ⊃ C)

Sierra is hearty only if Budweiser is bland, given that both Heineken is balanced and Michelob is complex.

(H • M) ⊃ (S ⊃ B)

Budweiser is bland if either Heineken is balanced or Foster's is refreshing.

(H ∨ F) ⊃ B

Michelob's being complex is a necessary condition for Heineken's being balanced unless Alaskan's being sweet is a sufficient condition for Carlsberg's being malty.

(H ⊃ M) ∨ (A ⊃ C)

Sierra is hearty given that Michelob's being flavorful implies that Guinness is heavy.

(M ⊃ G) ⊃ S

Princess and Azmara improve gym facilities only if neither Carnival controls rowdiness nor Seabourn reduces fares.

(P • A) ⊃ ∼(C ∨ S)

Princess drops its dress codes or Oceania enlarges its fleet, and Seabourn reduces its fares.

(P ∨ O) • S

Corona is drinkable if Pabst is clean tasting, and Foster's is refreshing only if Guinness is dark.

(P ⊃ C) • (F ⊃ G)

Azmara's opening new boutiques is a sufficient and necessary condition for both Norwegian's improving entertainment and Holland's remodeling its staterooms if Princess's dropping its dress codes implies that Celebrity revises its itineraries.

(P ⊃ C) ⊃ [A ≡ (N • H)]

1. S ∨ (∼Q ∨ ∼C) 2. (∼Q ∨ ∼C) ⊃ M 3. T ⊃ (Q • C)

(S ∨ ∼Q) ∨ C 1, Assoc

1. R ⊃ (E • D) 2. R • ∼G 3. ∼E ⊃ G

Add

1. ∼M ⊃ S 2. ∼M 3. (M ∨ H) ∨ ∼S

Assoc

Given the following premises: 1. T ∨ S 2. A ⊃ T 3. A • (∼T • S)

Assoc

1. (S ⊃ ∼F) • (∼F ⊃ B) 2. S ∨ ∼F 3. ∼F

CD

Given the following premises: 1. ∼N ∨ H 2. Q ⊃ ∼(∼N ∨ H) 3. (∼N ⊃ Q) • (H ⊃ Q)

CD

D ∨ M (M ⊃ A) • (D ⊃ C) -------------------- A ∨ C

CD—valid.

These statements are: P ≡ (S ∨ ∼ A) / A ⊃ (M • J) / J ⊃ (P • S) / J ≡ A

Consistent

∼M M ⊃ ∼G --------- G

DA—invalid

1. ∼R ∨ ∼R 2. R ∨ (∼J • ∼H) 3. ∼R ⊃ (H • B)

DM

1. Q ⊃ (∼N ∨ ∼N) 2. ∼N ⊃ ∼∼P 3. P ⊃ ∼G

DN

1. (E ⊃ K) ∨ W 2. ∼W 3. W ∨ ∼(Q ⊃ E)

DS

Given the following premises: 1. ∼∼N 2. K ⊃ ∼N 3. ∼N ∨ (K • S)

DS

1. (K • ∼T) ∨ (K • ∼H) 2. ∼M ⊃ (K • ∼H) 3. ∼(K • ∼H)

Dist

1. (∼H • ∼J) ⊃ K 2. ∼(∼H • ∼J) 3. (∼H • N) ∨ (∼H • ∼J)

Dist

Given the following premises: 1. ∼N • ∼F 2. K ⊃ (N • F) 3. U ∨ (K • ∼N)

Dist

In Proposition 2C, the main operator is:

Dot

The truth table for Statement 2B has how many lines? [N ≡ (S • J)] ⊃ [S ⊃ (N ⊃ J)]

Eight

1. (S • ∼J) ∨ (∼S • ∼∼J) 2. S ∨ ∼S 3. ∼J ⊃ P

Equiv

Given the following premises: 1. ∼(G • F) 2. ∼F ⊃ H 3. (G ⊃ ∼F) • (∼F ⊃ G)

Equiv

1. (C • ∼F) ⊃ E 2. G ∨ (C • ∼F) 3. ∼(C • ∼F)

Exp

Given the following premises: 1. E 2. R ⊃ ∼E 3. N ⊃ (∼C ⊃ R)

Exp

Given the following premises: 1. N ≡ R 2. (N • ∼R) ⊃ C 3. N

Exp

Given the following premises: 1. ∼(F • J) 2. ∼F 3. (F • H) ∨ (F • J)

F • (H ∨ J) 3, Dist

What is the truth value of Proposition 1B.

False

What is the truth value of Proposition 2A. [(X ⊃ A) • (B ⊃ ∼ Y)] ⊃ [(B ∨ Y) • (A ⊃ X)]

False

What is the truth value of Proposition 2C

False

The truth table for Statement 1A has how many lines? (N ⊃ K) ≡ (K ⊃ N)

Four

The truth table for Statement 1B has how many lines? (R • B) ≡ (B ⊃ ∼ R)

Four

Harp is soothing if and only if both Miller is not zesty and Coors is not smooth.

H ≡ (∼M • ∼C)

Given the following premises: 1. P • (∼H ∨ D) 2. ∼(∼P • ∼H) 3. (P ⊃ ∼H) • (∼P ⊃ H)

Impl

Given the following premises: 1. T ⊃ (G ∨ G) 2. ∼P ⊃ T 3. F ⊃ (B ⊃ ∼P)

Impl

Given the following premises: 1. ∼T ⊃ E 2. ∼K ⊃ (∼T ∨ ∼T) 3. M ⊃ (∼K ∨ ∼L)

Impl

Given the pair of statements: D • ∼ R and R • ∼ D

Inconsistent

These statements are: C • ∼ L and L • ∼ C

Inconsistent

These statements are: P ⊃ (A ⊃ M) / (D ∨ K) ⊃ (M ⊃ H) / (A • ∼ H) ∨ ∼ D / P • D

Inconsistent

These statements are: R ⊃ (Q ∨ ∼ N) / Q ⊃ (U ⊃ ∼ B) / B ⊃ (N • U) / R • B

Inconsistent

These statements are: S ⊃ (Q ∨ L) / (Q ∨ G) ⊃ (S ⊃ N) / L ⊃ (N ∨ ∼ S) / S • ∼ N

Inconsistent

(∼G ∨ E) • (R ∨ M) R ∨ ∼G ------------------- E ∨ M

Invalid

D ∨ ∼E ∼E -------- D

Invalid

K ⊃ R E ⊃ R ------ K ⊃ E

Invalid

This argument is: Q ∨ ∼S / ∼(N • A) / S ∨ A / (P • N) ∨ (G • Q) // P • G

Invalid

This argument is: P ∨ J / ∼(J • ∼ P) // J ≡ ∼ P

Invalid; fails in 1st line.

This argument is: S ≡ (N ∨ H) / S ∨ ∼N // S ⊃ H

Invalid; fails in 2nd line.

This argument is: K ⊃ (M ∨ ∼ H) / M ⊃ H / M ⊃ K // K ⊃ H

Invalid; fails in 4th line.

Given the pair of statements: ∼ (S ⊃ Q) and ∼ Q • S

Logically equivalent

Given the following premises: 1. K ∨ ∼H 2. (K ∨ ∼H) ⊃ (B ⊃ J) 3. J ⊃ D

MP

Given the following premises: 1. N ∨ C 2. (N ∨ C) ⊃ (F ⊃ C) 3. ∼C

MP

S ∨ ∼T S -------- ∼T

MP - Valid

∼S ∼S ⊃ F ------- F

MP - valid

G ⊃ ∼R G -------- ∼R

MP — valid

∼K ⊃ ∼N ∼K ---------- ∼N

MP—valid.

Given the following premises: 1. P ⊃ L 2. ∼(J • O) 3. (L ⊃ A) ⊃ (J • O)

MT

∼H ⊃ ∼B B --------- H

MT - Valid

∼S ⊃ ∼F F --------- S

MT - Valid

H ⊃ ∼M M -------- ∼H

MT—valid

Either Azmara or Seabourn do not open new boutiques provided that Princess improves its cuisine.

P ⊃ (∼A ∨ ∼S)

1. R ⊃ (∼B ⊃ F) 2. ∼U ⊃ B 3. ∼B

R ⊃ (∼F ⊃ ∼∼B) 1, Trans

Given the following premises: 1. S ⊃ (∼∼T • ∼∼C) 2. (S • Q) ∨ C 3. ∼C

S ⊃ (T • ∼∼C) 1, DN

Given the following premises: 1. F ∨ S 2. ∼S 3. (S ⊃ W) • (F ⊃ N)

S ⊃ W 3, Simp

Given the statement: (A ∨ ∼ S) • (S • ∼ A)

Self Contradictory

Statement 1B is: (R • B) ≡ (B ⊃ ∼ R)

Self Contradictory

Statement 3A is: [∼ H ∨ (E • D)] ≡ [(H • ∼ E) ∨ (H • ∼ D)]

Self contradictory

Given the following premises: 1. (J • ∼N) ∨ T 2. ∼(J • ∼N) 3. ∼T

T 1, 2, DS

1. D ⊃ (∼A ∨ ∼A) 2. ∼A ⊃ (R • M) 3. ∼R • ∼M

Taut

1. ∼P 2. L ⊃ (P ∨ M) 3. (P • M) ⊃ (∼R ∨ ∼R)

Taut

Statement 1C Given the following statement: (H ∨ ∼ K) ≡ (K ⊃ H)

Tautologous

Statement 2A is: (G ⊃ ∼ Q) ≡ ∼(Q • G)

Tautologous

Statement 2B is: [N ≡ (S • J)] ⊃ [S ⊃ (N ⊃ J)]

Tautologous

What is the truth value of Proposition 1A.

True

What is the truth value of Proposition 1C. ∼{[(B ≡ ∼X) ⊃ Y]∨[∼ X ⊃ (A ⊃ Y)]}

True

What is the truth value of Proposition 2B. [(A ⊃ Y) ≡ (B ⊃ ∼X)] ∨ ∼[(B • ∼ X) ≡ (Y • A)]

True

Given the argument: R ∨ I / ∼ S ∨ (R ⊃ I) // S ⊃ I

Valid

This argument is: (K • ∼ C) ⊃ ∼(P • R) / J ⊃ (K • P) / A ⊃ (P • R) // (A • J) ⊃ C

Valid

This argument is: B ∨ M / B ∨ ∼ K // (K ∨ ∼ M) ⊃ B

Valid

This argument is: J ⊃ C / R ∨ I / I ⊃ (U • ∼ J) / (R ∨ U) ⊃ (C • J) // C

Valid

Sierra's being hearty is a necessary condition for both Coors's being smooth and Harp's being crisp; moreover, Guinness is dark if and only if Alaskan's being sweet implies that Beck's is subtle.

[(C • H) ⊃ S] • [G ≡ (A ⊃ B)]

(p ⊃ q) • (r ⊃ s) ∼ q ∨ ∼ s ----------------- ∼ p ∨ ∼ r

destructive dilemma (DD) valid

The truth table for Statement 3A has how many lines? [∼ H ∨ (E • D)] ≡ [(H • ∼ E) ∨ (H • ∼ D)]

eight

p ⊃ q q ⊃ r ------ p ⊃ r

hypothetical syllogism (HS) valid

≡ (Triple Bar)

if and only if, is a sufficient and necessary condition for (equivalence)

⊃ (Horseshoe)

if... then... , only if, implies (implication)

Given the pair of statements: ∼ (H ≡ R) and ∼ (R ⊃ ∼ H)

inconsistent

E ⊃ ∼A B ⊃ ∼E ------- B ⊃ A

invalid

This argument is: C ⊃ ∼ M / I ⊃ ∼ H / (N • I) ∨ (G • C) / H ∨ M // G • M

invalid

This argument is: E ⊃ J / B ⊃ Q / D ⊃ (J • ∼ Q) // (E • B) ≡ D

invalid

p ⊃ q p ------ q

modus ponens (MP) valid

p ⊃ q ∼q ------- ∼p

modus tollens (MT) valid

∼ (Tilde)

not, it is not the case that (negation)

∨ (Wedge)

or, unless (disjunction)

In Proposition 2B, the main operator is: [(A ⊃ Y) ≡ (B ⊃ ∼X)] ∨ ∼[(B • ∼ X) ≡ (Y • A)]

wedge

1. Q ⊃ (H • ∼F) 2. ∼(Q • ∼M) 3. ∼G ⊃ (Q • ∼M)

∼Q ∨ ∼∼M 2, DM

Given the following premises: 1. ∼(Q • ∼S) 2. ∼F ⊃ (Q • ∼S) 3. H ∨ (Q • ∼S)

∼∼F 1, 2, MT

Given the following premises: 1. F ⊃ J 2. A ⊃ (F • J) 3. A • (Q ∨ N)

3, Com

Alaskan is sweet only if neither Heineken is balanced nor Pabst is clean tasting.

A ⊃ ∼(H ∨ P)

L ∼N ⊃ L -------- ∼N

AC—invalid

∼B ⊃ ∼J ∼J --------- ∼B

AC—invalid.

Given the following premises: 1. N ⊃ ∼(S ∨ K) 2. S ∨ K 3. S ⊃ (R • Q)

Add

Coors is smooth or both Beck's is subtle and Guinness is heavy.

C ∨ (B • G)

Carnival advertises its parties if and only if Disney's promoting family cruises implies that Norwegian improves its entertainment.

C ≡ (D ⊃ N)

Given the following premises: 1. H ∨ M 2. E ⊃ ∼(H ∨ M) 3. (H ⊃ D) • (M ⊃ O)

CD

G ∨ ∼T (G ⊃ ∼H) • (∼T ⊃ A) -------------------- ∼H ∨ A

CD - Valid

(∼H ⊃ K) • (H ⊃ ∼T) H ∨ ∼H -------------------- ∼T ∨ K

CD—valid.

Given the following premises: 1. E ⊃ (B • J) 2. (J • B) ⊃ ∼L 3. L

Com

Given the following premises: 1. ∼E ⊃ P 2. ∼P 3. ∼(P ∨ ∼H)

Conj

These statements are: ∼ (R ≡ M) and M • ∼ R

Consistent

If Disney promotes family cruises, then if either Holland remodels its staterooms or Regent enlarges its casinos, then Windstar diversifies its activities.

D ⊃ [(H ∨ R) ⊃ W]

∼D ⊃ N D --------- ∼N

DA - invalid

∼Q ⊃ ∼R Q --------- R

DA - invalid

P ∨ G (H ⊃ ∼P) • (C⊃∼G) -------------------- ∼H ∨ ∼C

DD—valid

(R ⊃ ∼T) • (D ⊃ T) ∼T ∨ T ------------------ ∼R ∨ ∼D

DD—valid.

(∼C ⊃ ∼J) • (P ⊃ L) J ∨ ∼L ------------------ C ∨ ∼P

DD—valid.

Given the following premises: 1. ∼I ∨ ∼∼B 2. M ⊃ ∼I 3. I

DM

Given the following premises: 1. ∼R ≡ ˜R 2. N • ˜T 3. R ⊃ ˜(N • ˜T)

DM

Given the following premises: 1. ∼W 2. C ∨ W 3. R ⊃ ∼(C ∨ W)

DM

Given the following premises: 1. Q ⊃ (A ∨ ∼T) 2. T 3. A ∨ ∼T

DN

∼S ∨ ∼T T -------- ∼S

DS - valid

K ∨ ∼B B -------- K

DS—valid.

Given the following premises: 1. ∼(∼H • J) 2. K ∨ (∼H • J) 3. (M ∨ M) ⊃ (∼H • J)

Dist

Given the following premises: 1. ∼D ∨ ∼T 2. D ∨ (∼T • ∼R) 3. D

Dist

Not either Regent enlarges its casinos or Celebrity revises its itineraries if Holland remodels its staterooms.

H ⊃ ∼(R ∨ C)

F ⊃ ∼K ∼N ⊃ F -------- ∼N ⊃ ∼K

HS—valid.

∼D ⊃ ∼C R ⊃ ∼D --------- R ⊃ ∼C

HS—valid.

∼J ⊃ C C ⊃ ∼T -------- ∼J ⊃ ∼T

HS—valid.

In Proposition 2A, the main operator is: [(X ⊃ A) • (B ⊃ ∼ Y)] ⊃ [(B ∨ Y) • (A ⊃X)]

Horseshoe

Norwegian improves its entertainment only if both Disney does not promote family cruises and Windstar does not diversify its activities.

N ⊃ (∼D • ∼W)

In Proposition 1C, the main operator is: ∼{[(B ≡ ∼X) ⊃ Y] ∨ [∼X ⊃ (A ⊃Y)]}

Tilde

Given the following premises: 1. ∼A ⊃ ∼S 2. E ⊃ (∼Q ⊃ ∼A) 3. ∼Q

Trans

Main operator of proposition 1A

Triple Bar

This argument is: (K •∼C) ⊃ ∼(P•R) / J⊃(K • P) / A ⊃ (P • R) //(A • J) ⊃C

Valid


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