Propositional Logic: Logical Arguments and Soundness Online Test

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Propositional Logic: Logical Arguments and Soundness

Description: This quiz evaluates your understanding of propositional logic, logical arguments, and the concept of soundness.
Number of Questions: 15
Created by: Aliensbrain Bot
Tags: propositional logic logical arguments soundness

Which of the following is a propositional variable?

A
B
C
D

What is the truth value of the proposition "2 + 2 = 5"?

True
False

Which of the following is a logical connective?

And
Or
Not
If-then

What is the truth value of the compound proposition "(P ∧ Q) ∨ ¬R" if P is true, Q is false, and R is true?

True
False

Which of the following is a valid logical argument?

If it is raining, then the ground is wet.
The ground is wet, therefore it is raining.
If it is raining, then the sky is blue.
The sky is blue, therefore it is raining.

What is the difference between a sound and an unsound logical argument?

A sound argument has true premises and a true conclusion.
An unsound argument has false premises and a false conclusion.
A sound argument has true premises and a false conclusion.
An unsound argument has false premises and a true conclusion.

Which of the following is an example of a sound logical argument?

All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.
All dogs are mammals.
Cats are not dogs.
Therefore, cats are not mammals.

Which of the following is an example of an unsound logical argument?

All birds can fly.
Penguins are birds.
Therefore, penguins can fly.
All fruits contain seeds.
Tomatoes are fruits.
Therefore, tomatoes contain seeds.

What is the converse of the proposition "If it is raining, then the ground is wet"?

If the ground is wet, then it is raining.
If it is not raining, then the ground is not wet.
If the ground is not wet, then it is not raining.
If it is raining, then the ground is not wet.

What is the inverse of the proposition "If it is raining, then the ground is wet"?

If it is not raining, then the ground is not wet.
If the ground is wet, then it is raining.
If the ground is not wet, then it is not raining.
If it is raining, then the ground is not wet.

What is the contrapositive of the proposition "If it is raining, then the ground is wet"?

If the ground is wet, then it is raining.
If it is not raining, then the ground is not wet.
If the ground is not wet, then it is not raining.
If it is raining, then the ground is not wet.

Which of the following is a tautology?

(P ∨ ¬P)
(P ∧ ¬P)
(P → Q) ∨ (¬P → Q)
(P → Q) ∧ (¬P → ¬Q)

Which of the following is a contradiction?

(P ∨ ¬P)
(P ∧ ¬P)
(P → Q) ∨ (¬P → Q)
(P → Q) ∧ (¬P → ¬Q)

What is the law of detachment?

If P → Q and P, then Q.
If P → Q and ¬Q, then ¬P.
If P ∨ Q and P, then Q.
If P ∨ Q and ¬P, then Q.

What is the law of syllogism?

If P → Q and Q → R, then P → R.
If P → Q and ¬Q, then ¬P.
If P ∨ Q and P, then Q.
If P ∨ Q and ¬P, then Q.

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