Critical Reasoning: Key Concepts, Logic, and Probability for Midterm

When is the midterm exam for P105 Critical Reasoning?

March 12th, 2026

What types of questions will be on the midterm exam?

True/false, short answers, definitions, and longer answer questions.

What is System 1 thinking characterized by?

Fast, frugal, automatic, and non-transparent.

What is System 2 thinking characterized by?

Slow, deliberate, and transparent.

Give an example of System 1 thinking.

Recognizing faces.

Give an example of System 2 thinking.

Doing multiplication in your head.

What is the base rate fallacy?

Ignoring the base rate in probability assessments.

What is the conjunction fallacy?

Assuming that specific conditions are more probable than a single general one.

What is the availability heuristic?

Overestimating the probability of events based on how easily examples come to mind.

What is the anchoring effect?

Relying too heavily on the first piece of information encountered.

What does it mean for an argument to be deductively valid?

If all premises are true, the conclusion must also be true.

What is a tautology?

A formula that is true in every possible interpretation.

What is a contradiction?

A formula that is false in every possible interpretation.

What are the three laws of probability?

Non-negativity, normalization, and additivity.

How do you compute the probability of a disjunction?

Using the formula p(A ∨ B) = p(A) + p(B) for mutually exclusive events.

What is conditional probability?

The probability of an event given that another event has occurred.

What is the formula for conditional probability?

p(A|B) = p(A ∧ B) / p(B).

What is the probability that a randomly selected student passed the midterm, given that they completed the extra credit?

3/4.

What does it mean for two formulas to be logically equivalent?

They have the same truth value in every possible interpretation.

What is the significance of truth tables in propositional logic?

They are used to determine the validity of arguments and the nature of logical formulas.

What is the conclusion of the argument: If it is raining, then the game will be cancelled. It is raining. Therefore, the game will be cancelled?

The game will be cancelled.

What is the conclusion of the argument: All mammals are warm-blooded. Whales are mammals. So, whales are warm-blooded?

Whales are warm-blooded.

What is the base rate in the context of a disease test?

The probability of having the disease before considering the test result.

What is the result of the argument: P → Q, ¬P therefore ¬Q?

Invalid.

What is the result of the argument: P ∨ Q, ¬P therefore Q?

Valid.

What is the truth value of P ∨ ¬P?

True in every case.

Is ¬(P ∧ Q) logically equivalent to (¬P ∨ ¬Q)?

Yes.