Propositional Logic - 1.1

What is a proposition?

A fact that is either T or F. Not both.

Can variables be a proposition?

No! Because their values can change, which changes the "fact".

What is the English phrase for "Negation"?

not p

Which compound proposition does this symbol represent? ¬

Negation

Which compound proposition does this symbol represent? ∧

Conjunction

What is the English phrase for "conjunction"?

and

What's a phrase to help remember the truth table for CONJUNCTION?

Only T if BOTH are T. Otherwise F.

What's a phrase to help remember the truth table for NEGATION?

The opposite of the original variable.

Which compound proposition does this symbol represent? v

Disjunction

What is the English phrase disjunction"?

or

What's a phrase to help remember the truth table for DISJUNCTION?

T when at least ONE of the propositions are T.

Is disjunction INCLUSIVE or or EXCLUSIVE or?

inclusive or

Which compound proposition does this symbol represent?⊕

Exclusive or

What's a phrase/example to help remember the truth table for EXCLUSIVE OR?

Only ONE (of p or q) can be T for the statement to be T. At a restaurant, can only have a soup or salad, not both.

What's an example to help remember the truth table for INCLUSIVE OR?

Have to take math or science as a pre-req for a course. Can take either one or both to take the course.

Which compound proposition does this symbol represent? →

Implication or conditional statement

What's a phrase/example to help remember the truth table for implication?

Fake a true world:
In a T world, only a truth can be told for the situation to be T.
In a F world, anything can be said and it will always be T.

What is the English phrase "implication"?

if ___, then ___

For implication, what are the other ways of saying "p"?

premise, hypothesis or antecedent

For implication, what are the other ways of saying "q"?

conclusion or consequence

What is converse?

q → p

What is inverse?

¬ p → ¬ q

What is contrapositive?

¬ q → ¬ p

What is this called? ¬ q → ¬ p

Contrapositive

What is this called? ¬ p → ¬ q

inverse

What is this called? q → p

converse

What is the English phrase "biconditional"?

___ if and only if ___

What's a phrase/example to remember the truth table for biconditional?

The plane example (p: fall through air, q: gravity is 10) OR only T when BOTH are T.

How many rows are there in a truth table with n propositional variables?

2^n

What is the precedence of logical operators?

Negation, Conjunction, Disjunction, Implication, Biconditional