Propositions are true or false

E vents occur or do not occur

To the union of two sets of events,

A U B

To the intersection of two sets of events,

A ∩ B

Pr ( )

If A and B are mutually exlusive, Pr (AvB)=?

Pr (A) + Pr (B)

You cannot add if the events or propositions __________.

Overlap

Two events are independent when what?

The occurrence of one does not influence the probability of the occurrence of the other

The truth of one does not make the truth of the other any more or less probable

So if A and B are independent, Pr (A&B)=?

Pr(A) x Pr(B)

Here is an example of either a conditional or categorical probability: which is it?

The probability that there will be a bumper grain croop next summer, given that there has been very heavy snowfall the previous winter

Conditional probability

What is this an example of: a categorical or conditional probability?

The probability of dealing an ace as the second card from a standard pack of well-shuffled cards (regardless of what card is dealt first)

What is this an example of (a categorical probability or a conditional probability?

Pr (S wins the final)=0.4

Pr (second card dealt is an ace) = 1/13

Categorical probability

What is this an example of: a categorical probability or conditional probability?

Pr (S wins his semifinal/ I loses his semifinal)= 0.5

Pr (second card dealt is an ace/first card dealt is a king)= 4/51

Conditiional probability

What does the definition of a conditional probability look like in mathematical terms?

Foreword pg xi

When Pr(B) > 0

Pr (A/B) = Pr (A&B)/ Pr(B)

Pr(B) must be a positive number

What are some characteristics of deductive reasoning?

Foreword pg xi

When you have true premises and a valid argument, the conclusion must be true too

Valid deductive arguments do not take risks

What are some characteristics of inductive logic?

It takes risks

You can have true premises, a good arguments, but a false conclusion

What do logicians study?

Arguments

An argument divides up into what and what?

Premises and a conclusion

What is a premise?

A point or series of reasons

What are propositions?

Premises and conclusions are

Statements that can be either true or false

What are two things that can go wrong with an argument?

The premises may be false

The premises may not provide a good reason for the conclusion

Identify these statements: which one are the premises and which one is the conclusion:

If James wants a job, then he will get a haircut tomorrow

James will get a haircut tomrrow

So:

James wants a job

The first two propositions are the premises

The third proposition is the conclusion

What is the definition of a fallacy?

Logicians use this term when there is a common error in reasoning

What is this an example of?

If A, then C

This is a fallacy of affirming the consequent

What are two basic ways to criticize an argument?

Challenge the premises--show that at least one is false

Challenge the reasoning--show that the premises are not a good reason for the conclusion

What can logic not tell and what can logic can tell?

It cannot tell whether premises are true or false

It can only tell whether the reasoning is good or bad

How would we define a valid argument from a Logicians standpoint?

It is logically impossible for the conclusion to be false given that the premises are true

Look at this example: is the conclusion true and false and is this valid or invalid?

• Every automobile sold by Queen Street Motors is rust-proofed
• Barbar's car is rust-proofed                                                Therefore:
• Barbara's car was sold by Queen Street Motors

Fill in the blanks: In logic,

__________ are true or false

___________ are valid or invalid

Propositions

Arguments

An argument is valid if and only if ?

the corresponding conditional proposition is a truth of logic

Valid arguments are _________ arguments

Risk-free

What does truth-preserving mean?

Whenever you start out with true premises, you will end up with a true conclusion

When do we say that an argument is sound?

All the premises are true and when the argument is valid

A valid argument never takes you from ____ ________to a ______  _________.

true premises

false conclusion

When can an argument be unsound?

When a premise is false and when the argument is invalid

A valid argument can have a ______ _______ but a _______ __________.

False premise

True conclusion

Validity is about the connection between ________ and __________, not about ________ or ___________

Truth or falsehood

What are the two ways to criticize a deduction?

A premise is false

The argument is invalid

Who is an expert on validity?

A logician

A risky argument can be a very good one, and yet its ________ can be false, even when the _________ are true 

conclusion

premises

Statement about a sample drawn from a given population

So:

Statement about the population as a whole

Or vice versa

Statemenbt about a sample

So:

Statement about a new sample

both at the same time

sum of their probabilities