Conceptual
If a set of statements is inconsistent, then it must be the case that at least one of those statements is false.
True
Determine whether each of the following statements is a tautology, a contradiction, or a contingent statement by constructing a truth table.
((P & Q) v ~(P & Q))
Tautology
If Louise is not Bob’s daughter, then she isn’t Linda’s daughter.
Let B = Louise is Bob’s daughter.
L = Louise is Linda’s daughter.
(~B --> ~L)
Determine how each of the following arguments fares with respect to our four criteria.
The following argument is inductive:
1. The vast majority of human beings have one lung.
2. Thainá is human being.
3. Therefore, Thainá has one lung
A deductive argument is invalid if and only if it is logically possible for the premises to be true and the conclusion false.
True
A deductive argument is an argument that is intended to be such that if the premises of the argument are true, then the conclusion is necessarily true.
True
Determine whether the following pairs of sentences are logically equivalent by constructing a truth table.
(P & ~Q); ((P & ~Q) & (P v ~P))
Equivalent
Hollyhock will continue speaking to Bojack only if Bojack doesn’t self-destruct.
Let B = Bojack self-destructs
H = Hollyhock continues speaking to Bojack.
(H --> ~B)
Determine how each of the following arguments fares with respect to our four criteria. The following argument is deductive:
1. Some cats are handbags.
2. Some handbags are dinosaurs.
3. Therefore, Some cats are dinosaurs.
Muriel is surely doomed if either Katz or the duck from space doesn’t fail to succeed.
Let K = Katz succeeds.
D = the duck from space succeeds.
M = Muriel is surely doomed.
((~ ~K v ~ ~ D) --> M)
If a premise of an inductive argument is irrelevant to the conclusion of that argument, then that argument must be weak.
False
Determine whether each of the following statements is a tautology, a contradiction, or a contingent statement by constructing a truth table.
(P <--> (Q v (P & ~R)))
Contingent
Dexter loves DeeDee if both DeeDee doesn’t enter his laboratory and she doesn’t tell Mom about his laboratory.
Let X = Dexter loves DeeDee.
E = DeeDee enters Dexter’s laboratory.
T = DeeDee tells Mom about Dexter’s laboratory.
((~E & ~T) --> X)
Determine how each of the following arguments fares with respect to our four criteria. The following argument is deductive:
1. Salvador either likes Plato or he doesn’t.
2. Thainá either likes Kripke or she doesn’t.
3. Therefore, Jordan either likes Russell or he doesn’t.
Determine whether the following deductive arguments are valid or invalid:
1. Some chefs are bakers
2. Some bakers are axe throwers
3. All axe throwers bake
4. Therefore, some chefs are axe throwers
Invalid
If a deductive argument is valid, then it is not possible for any of its premises to be false.
False
Determine whether the following arguments are TFL-valid or TFL-invalid by constructing a truth table.
(P <--> (~Q v R)). (R <--> ~P) ∴ ~P
Both Tina and Louise are Bob’s daughters only if both Gene is Bob’s son and Linda isn’t married to Hugo.
Let T = Tina is Bob’s daughter.
L= Louise is Bob’s daughter.
G = Gene is Bob’s son.
H = Linda is married to Hugo.
((T & L) --> (G & ~H))
Determine how the following deductive argument fares with respect to our four criteria of evaluation. Select all answers that apply.
1. Snow is black.
2. Therefore, snow is black.
Satisfies Criterion 2
Satisfies Criterion 3
Construct a deductive argument with the following features:
An invalid argument with true premises and a true conclusion.
Example:
1. The sky is blue
2. Grass is green
3. Therefore, Coffee is bitter
If a deductive argument has (actually) false premises and an (actually) false conclusion, then that argument cannot be valid.
False
Translate the following argument into TFL. Once you have done so, then construct a truth-table to determine if the argument is valid or invalid.
Only if Steven will save the day will both Gold Diamond and Blue Diamond fail to destroy Earth. Since Steven will save the day, it follows that either Gold Diamond or Blue Diamond will fail to destroy Earth.
If both Gold Diamond and Blue Diamond will fail to destroy the Earth, then Steven will save the day.
Steven will save the day.
Therefore, Gold Diamond will fail to destroy Earth.
Let G = Gold Diamond will destroy Earth.
B = Blue Diamond will destroy Earth.
S = Steven will save the day.
1. ((~G & ~B) --> S)
2. S
3. (conclusion) ~G v ~B
Invalid
Assuming that Katz doesn’t cover his bases, then provided that Ramses gets his slab back, then given that Muriel is safe if Courage saves the day, then Eustace can talk to his brother Horst.
Let P = Katz covers his bases
Q = Ramses gets his slab back
R = Muriel is safe
S = Courage saves the day
T = Eustace can talk to his brother Horst.
(~P --> (Q --> ((S --> R) --> T)))
Determine how the following deductive argument fares with respect to our four criteria of evaluation. Select all answers that apply.
1. It is impossible for a valid argument to have false premises
2. It is possible for a valid argument to have false premises.
3. Therefore, this argument is valid
Satisfies Criterion 2
Satisfies Criterion 3
Satisfies Criterion 4
Determine how the following deductive argument fares with respect to our four criteria of evaluation.
1. One in 750 people is born with only one kidney. (Assume this is true.)
2. There is a fair, 9-sided die with the numbers 1-9 evenly distributed on its faces. (Assume this is true.)
3. Jordan is a human being.
4. Therefore, the next time that a fair, 9-sided die with numbers 1-9 evenly distributed on its faces is rolled, it will land on an odd number.
Passes criterion 1.
Passes criterion 2.
Fails criterion 3.
Passes criterion 4.