Logic Final (Quizzes 4 & 5)
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
