Logics Mod 5
~D ⊃ ~C R ⊃ ~D R ⊃ ~C
HS valid
S v ~T S ~T
Invalid
Proposition 2B Given the following proposition: [(A ⊃ Y) ≡ (B ⊃ ~X)] v ~[(B · ~X) ≡ (Y · A)] Given that A and B are true and X and Y are false, determine the truth value of Proposition 2B
True
Movado's offering an ivory dial is a sufficient condition for Breitling's having a ruby model if Gucci's offering a better warranty is a necessary condition for Fossil's being water resistant
(F ⊃ G) ⊃ (M ⊃ B)
Movado and Nautica offer a black dial if and only if Piaget has a gold watch
(M · N) ≡ P
Given the following proposition: ~[(A v ~ B) ⊃ X] ⊃ [~Y ⊃ (A · X)] In Proposition 1B, the main operator is a
Horseshoe
D v ~E ~E D
Invalid
Given the argument: E ⊃ J / B ⊃ Q / D ⊃ (J · ~Q) // (E · B) ≡ D This argument is
Invalid
Not both Travelers and Conseco run an ad if Liberty opens new offices
L>~(T*C)
H ⊃ ~M M ~H
MT - valid
Piaget has a gold watch only if both Seiko has leather bands and Breitling has a diamond model
P ⊃ (S · B)
Either Azmara or Seabourn do not open new boutiques provided that Princess improves its cuisine
P ⊃ (~A v ~S)
Given the pair of statements: ~(R ≡ M) and M · ~R These statements are
Consistent
Q=~A and A*~Q
Consistent
(~C ⊃ ~J) · (P ⊃ L) J v ~L C v ~P
DD valid
~N v A N A
DS valid
Statement 1B Given the following statement: (R · B) ≡ (B ⊃ ~ R) The truth table for Statement 1B has how many lines
four
Gucci features stainless steel; also, Fossil is water resistant given that Cartier offers a stop watch
G · (C ⊃ F)
If either Nationwide or Geico does not open new offices, then Metropolitan does not hire agents
(~Nv~G)>~M
If Movado offers a blue dial, then neither Fossil is water resistant nor Nautica promotes a titanium case
M ⊃ ~(F v N)
Given the following statement: (R · B) ≡ (B ⊃ ~ R) Statement 1B is
Self-contradictory
Statement 1B Given the following statement: (R · B) ≡ (B ⊃ ~ R) Statement 1B is
Self-contradictory
Statement 3A Given the following statement: [~H v (E · D)] ≡ [(H · ~E) v (H · ~D)] Statement 3A is
Self-contradictory
Given the pair of statements: G v ~H and H v ~G These statements are
Consistent
~D ⊃ N D ~N
DA - invalid
~M M ⊃ ~G G
DA Invalid
~M M ⊃ ~G G
DA invalid
(R ⊃ ~T) · (D ⊃ T) ~T v T ~R v ~D
DD - valid
Given the following statement: [N ≡ (S · J)] ⊃ [S ⊃ (N ⊃ J)] The truth table for Statement 2B has how many lines
Eight
Proposition 2A Given the following proposition: [(X ⊃ A) · (B ⊃ ~Y)] ⊃ [(B v Y) · (A ⊃ X)] In Proposition 2A, the main operator is a
Horseshoe
[(X ⊃ A) · (B ⊃ ~Y)] ⊃ [(B v Y) · (A ⊃ X)] In Proposition 2A, the main operator is a
Horseshoe
Given the pair of statements: C · ~L and L · ~C These statements are
Inconsistent
Given the pair of statements: D · ~R and R · ~D These statements are
Inconsistent
Given the pair of statements: M*~D and D*~M
Inconsistent
Given the statements: S ⊃ (Q v L) / (Q v G) ⊃ (S ⊃ N) / L ⊃ (N v ~S) / S · ~N These statements are
Inconsistent
Given the statements: S ⊃ (Q v L) / (Q v G) ⊃ (S ⊃ N) / L ⊃ (N v ~S) / S · ~N These statements are:
Inconsistent
Given the pair of statements: ~(S ⊃ Q) and ~Q · S These statements are
Logically equivalent
Given the pair of statements: ~(S ⊃ Q) and ~Q · S These statements are:
Logically equivalent
~S ~S ⊃ F F
MP - valid
~K ⊃ ~N ~K ~N
MP Valid
~K ⊃ ~N ~K ~N
MP valid
Given the following statement: (N ⊃ K) ≡ (K ⊃ N) The truth table for Statement 1A has how many lines
Four
Given the following statement: (R · B) ≡ (B ⊃ ~ R) The truth table for Statement 1B has how many lines
Four
Statement 2B Given the following statement: [N ≡ (S · J)] ⊃ [S ⊃ (N ⊃ J)] Statement 2B is
Tautologous
Cartier's offering a stop watch implies that Seiko has leather bands, provided that both Rado advertises a calendar model and Tissot has luminous hands
(R · T) ⊃ (C ⊃ S)
If Tissot has luminous hands, then if either Rado advertises a calendar model or Fossil is water resistant, then Gucci features stainless steel
T ⊃ [(R v F) ⊃ G]
Given the following statement: [N ≡ (S · J)] ⊃ [S ⊃ (N ⊃ J)] Statement 2B is
Tautologous
Statement 2A Given the following statement: (G ⊃ ~Q) ≡ ~(Q · G) Statement 2A is
Tautologous
Use an ordinary truth table to answer the following problems. Construct the truth table as per the instructions in the textbook. Statement 2A Given the following statement: (G ⊃ ~Q) ≡ ~(Q · G) Statement 2A is:
Tautologous
Given the following proposition: [A ⊃ ~(B · Y)] ≡ ~[B ⊃ (X · ~A)] In Proposition 1A, the main operator is a
Triple
Proposition 1A Given the following proposition: [A ⊃ ~(B · Y)] ≡ ~[B ⊃ (X · ~A)] In Proposition 1A, the main operator is a
Triple bar
Given the following proposition: [(A ⊃ Y) ≡ (B ⊃ ~X)] v ~[(B · ~X) ≡ (Y · A)] Given that A and B are true and X and Y are false, determine the truth value of Proposition 2B
True
Proposition 1A Given the following proposition: [A ⊃ ~(B · Y)] ≡ ~[B ⊃ (X · ~A)] Given that A and B are true and X and Y are false, determine the truth value of Proposition 1A
True
(~G v E) · (R v M) R v ~G E v M
Invalid
Given the argument: Q v ~S / ~(N · A) / S v A / (P · N) v (G · Q) // P · G This argument is
Invalid
Either Breitling has a diamond model and Rado advertises a calendar watch or Tissot has luminous hands
(B · R) v T
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)
Princess drops its dress codes or Oceania enlarges its fleet, and Seabourn reduces its fares
(P v O) · S
Princess and Azmara improve gym facilities only if neither Carnival controls rowdiness nor Seabourn reduces fares
(P · A) ⊃ ~(C v S)
Given the following premises: 1. (S ⊃ R) ⊃ (J ⊃ T) 2. (P ⊃ R) ⊃ (S ⊃ R) 3. R ⊃ J
(P ⊃ R) ⊃ (J ⊃ T) 1, 2, HS
Either Safeco reduces premiums and Geico cuts costs or Farmers hires agents.
(S*G)vF
Carnival advertises its parties if and only if Disney's promoting family cruises implies that Norwegian improves its entertainment
C ≡ (D ⊃ N)
Use indirect truth tables to answer the following problems. Given the argument: E ⊃ J / B ⊃ Q / D ⊃ (J · ~Q) // (E · B) ≡ D This argument is:
Invalid
Given the pair of statements: Q=~A and A*~Q These statements are
Consistent
Given the statements: Q ⊃ (N v S) / N ⊃ (L ⊃ B) / (S v E) ⊃ (Q ⊃ B) / Q ≡ ~B These statements are
Consistent
Given the statement: (F v ~ S) ⊃ ~(S v ~F) This statement is
Contingent
Use an ordinary truth table to answer the following problems. Construct the truth table as per the instructions in the textbook. Given the statement: (F v ~ S) ⊃ ~(S v ~F) This statement is
Contingent
Given the pair of statements: J ≡ ~M and (J · M) v ~(M v J) These statements are
Contradictory
If Disney promotes family cruises, then if either Holland remodels its staterooms or Regent enlarges its casinos, then Windstar diversifies its activities
D ⊃ [(H v R) ⊃ W]
Given the following statement: [~H v (E · D)] ≡ [(H · ~E) v (H · ~D)] The truth table for Statement 3A has how many lines
Eight
Statement 2B Given the following statement: [N ≡ (S · J)] ⊃ [S ⊃ (N ⊃ J)] The truth table for Statement 2B has how many lines
Eight
Statement 3A Given the following statement: [~H v (E · D)] ≡ [(H · ~E) v (H · ~D)] The truth table for Statement 3A has how many lines
Eight
Given the following premises: 1. N v C 2. (N v C) ⊃ (F ⊃ C) 3. ~C
F ⊃ C 1, 2, MP
Given the following proposition: [(X ⊃ A) · (B ⊃ ~Y)] ⊃ [(B v Y) · (A ⊃ X)] Given that A and B are true and X and Y are false, determine the truth value of Proposition 2A
False
Given the following proposition: ~[(A v ~ B) ⊃ X] ⊃ [~Y ⊃ (A · X)] Given that A and B are true and X and Y are false, determine the truth value of Proposition 1B
False
Proposition 1B Given the following proposition: ~[(A v ~ B) ⊃ X] ⊃ [~Y ⊃ (A · X)] Given that A and B are true and X and Y are false, determine the truth value of Proposition 1B
False
Statement 1A Given the following statement: (N ⊃ K) ≡ (K ⊃ N) The truth table for Statement 1A has how many lines
Four
Use an ordinary truth table to answer the following problems. Construct the truth table as per the instructions in the textbook. Statement 1B Given the following statement: (R · B) ≡ (B ⊃ ~ R) The truth table for Statement 1B has how many lines
Four
Not either Regent enlarges its casinos or Celebrity revises its itineraries if Holland remodels its staterooms
H ⊃ ~(R v C)
Given the following proposition: [(X ⊃ A) · (B ⊃ ~Y)] ⊃ [(B v Y) · (A ⊃ X)] In Proposition 2A, the main operator is a
Horseshoe
M*~D and D*~M
Inconsistent
Norwegian improves its entertainment only if both Disney does not promote family cruises and Windstar does not diversify its activities
N ⊃ (~D · ~W)
Progressive expands coverage if and only if both Liberty and Conseco do not cut costs
P=(~L*~C)
Given the following proposition: [A ⊃ ~(B · Y)] ≡ ~[B ⊃ (X · ~A)] Given that A and B are true and X and Y are false, determine the truth value of Proposition 1A
True
Given the argument: (K · ~C) ⊃ ~(P · R) / J ⊃ (K · P) / A ⊃ (P · R) // (A · J) ⊃ C This argument is
Valid
Given the argument: J ⊃ C / R v I / I ⊃ (U · ~J) / (R v U) ⊃ (C · J) // C This argument is
Valid
Use indirect truth tables to answer the following problems. Given the argument: J ⊃ C / R v I / I ⊃ (U · ~J) / (R v U) ⊃ (C · J) // C This argument is: Question 2 options:
Valid
Given the following premises: 1. ~I v ~~B 2. M ⊃ ~I 3. I
~(I · ~B) 1, DM
Given the following premises: 1. (E ⊃ K) v W 2. ~W 3. W v ~(Q ⊃ E)
~(Q ⊃ E) 2, 3, DS
Progressive increases its territory if neither Safeco cuts costs nor Travelers runs an ad
~(SvT)>P