Reasoning
Logic and Fallacies
1,716 Questions
Understand the fundamentals of propositional logic, logical inference rules, and paradoxes. This set includes identifying logical fallacies, including those found in classical Nyaya logic. Strong grasp of these concepts is crucial for scoring well in the reasoning sections of competitive tests.
Propositional logic modelsLogical inference rulesTypes of logical fallaciesParadoxes and contingent truthsNyaya logic concepts
Logic and Fallacies Questions
Which of the following is an example of a false dilemma fallacy?
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Either we go to war or we surrender.
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Either we raise taxes or we cut spending.
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Either we believe in God or we are atheists.
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Either we support the government or we are traitors.
A
Correct answer
Explanation
A false dilemma fallacy occurs when someone presents two options as the only two possible choices, when in reality there are other options available. In this case, the person is presenting the choice between going to war or surrendering as the only two options. However, there are other options available, such as negotiating a peace treaty or engaging in diplomacy.
Which of the following is an example of an ad hominem fallacy?
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You can't trust what he says because he's a liar.
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You can't trust what she says because she's a thief.
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You can't trust what he says because he's a communist.
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You can't trust what she says because she's a racist.
A
Correct answer
Explanation
An ad hominem fallacy occurs when someone attacks the person making an argument, rather than the argument itself. In this case, the person is attacking the person making the argument by calling them a liar. This is an ad hominem fallacy because it is an attack on the person, rather than the argument.
Which of the following is an example of a non sequitur fallacy?
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I like chocolate, therefore I like vanilla.
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The sky is blue, therefore the grass is green.
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The government is corrupt, therefore we should abolish the government.
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The economy is doing well, therefore we should re-elect the president.
A
Correct answer
Explanation
A non sequitur fallacy occurs when someone draws a conclusion that does not follow logically from the evidence presented. In this case, the person is drawing the conclusion that they like vanilla because they like chocolate. However, there is no logical connection between liking chocolate and liking vanilla. Therefore, this is a non sequitur fallacy.
What is the most common type of epistemic modal operator?
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The knowledge operator (K)
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The belief operator (B)
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The possibility operator (◇)
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The necessity operator (□)
A
Correct answer
Explanation
The knowledge operator (K) is the most common type of epistemic modal operator.
In epistemic logic, what does the operator (K) represent?
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Knowledge
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Belief
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Certainty
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Probability
A
Correct answer
Explanation
The operator (K) in epistemic logic is used to represent knowledge. It is used to express statements about what an agent knows to be true.
Which of the following is a valid inference rule in epistemic logic?
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\(K(p) \rightarrow K(K(p))\)
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\(K(p) \rightarrow p\)
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\(K(p) \wedge K(q) \rightarrow K(p \wedge q)\)
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\(K(p) \vee K(q) \rightarrow K(p \vee q)\)
A
Correct answer
Explanation
The inference rule (K(p) \rightarrow K(K(p))) is known as the rule of positive introspection. It states that if an agent knows something, then they also know that they know it. This rule is valid in epistemic logic because it is a fundamental property of knowledge that we are aware of what we know.
What is the formula for the law of necessitation?
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$ \vdash \phi \rightarrow \Box \phi $
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$ \vdash \Box \phi \rightarrow \phi $
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$ \vdash \phi \rightarrow \Diamond \phi $
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$ \vdash \Diamond \phi \rightarrow \phi $
A
Correct answer
Explanation
The law of necessitation states that if a formula is provable, then its necessity is also provable.
What is the formula for the law of distribution of disjunction over necessity?
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$ \Box (\phi \wedge \psi) \leftrightarrow \Box \phi \wedge \Box \psi $
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$ \Box (\phi \vee \psi) \leftrightarrow \Box \phi \vee \Box \psi $
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$ \Diamond (\phi \wedge \psi) \leftrightarrow \Diamond \phi \wedge \Diamond \psi $
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$ \Diamond (\phi \vee \psi) \leftrightarrow \Diamond \phi \vee \Diamond \psi $
B
Correct answer
Explanation
The law of distribution of disjunction over necessity states that the necessity of a disjunction is equivalent to the disjunction of the necessities.
What is the formula for the axiom of reflexivity for belief?
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$ \vdash B\phi \rightarrow \phi $
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$ \vdash \phi \rightarrow B\phi $
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$ \vdash \Diamond B\phi \rightarrow B\phi $
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$ \vdash B\phi \rightarrow \Diamond B\phi $
A
Correct answer
Explanation
The axiom of reflexivity for belief states that if an agent believes a proposition, then the proposition is true.
What is the formula for the axiom of positive introspection for belief?
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$ \vdash B\phi \rightarrow B B\phi $
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$ \vdash B B\phi \rightarrow B\phi $
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$ \vdash \Diamond B\phi \rightarrow B\phi $
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$ \vdash B\phi \rightarrow \Diamond B\phi $
A
Correct answer
Explanation
The axiom of positive introspection for belief states that if an agent believes a proposition, then the agent believes that they believe the proposition.
What is the formula for the axiom of negative introspection for belief?
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$ \vdash B\phi \rightarrow B B\phi $
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$ \vdash B B\phi \rightarrow B\phi $
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$ \vdash \Diamond B\phi \rightarrow B\phi $
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$ \vdash B\phi \rightarrow \Diamond B\phi $
Correct answer
Explanation
The axiom of negative introspection for belief states that if an agent does not believe a proposition, then the agent believes that they do not believe the proposition.
What is the formula for the rule of necessitation for belief?
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$ \vdash B\phi \rightarrow B \Box B\phi $
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$ \vdash B \Box B\phi \rightarrow B\phi $
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$ \vdash \Diamond B\phi \rightarrow B\phi $
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$ \vdash B\phi \rightarrow \Diamond B\phi $
A
Correct answer
Explanation
The rule of necessitation for belief states that if an agent believes a proposition, then the agent believes that it is necessary that they believe the proposition.
What is the formula for the rule of distribution of belief over conjunction?
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$ \vdash B(\phi \wedge \psi) \leftrightarrow (B\phi \wedge B\psi) $
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$ \vdash B(\phi \vee \psi) \leftrightarrow (B\phi \vee B\psi) $
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$ \vdash \Diamond B\phi \rightarrow B\phi $
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$ \vdash B\phi \rightarrow \Diamond B\phi $
A
Correct answer
Explanation
The rule of distribution of belief over conjunction states that an agent believes a conjunction if and only if the agent believes both conjuncts.
What is the formula for the rule of distribution of belief over disjunction?
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$ \vdash B(\phi \wedge \psi) \leftrightarrow (B\phi \wedge B\psi) $
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$ \vdash B(\phi \vee \psi) \leftrightarrow (B\phi \vee B\psi) $
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$ \vdash \Diamond B\phi \rightarrow B\phi $
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$ \vdash B\phi \rightarrow \Diamond B\phi $
B
Correct answer
Explanation
The rule of distribution of belief over disjunction states that an agent believes a disjunction if and only if the agent believes at least one disjunct.
What is the formula for the rule of generalization for belief?
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$ \vdash B\phi \rightarrow B \forall x \phi $
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$ \vdash B \forall x \phi \rightarrow B\phi $
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$ \vdash \Diamond B\phi \rightarrow B\phi $
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$ \vdash B\phi \rightarrow \Diamond B\phi $
A
Correct answer
Explanation
The rule of generalization for belief states that if an agent believes a proposition, then the agent believes the universal generalization of that proposition.