CSE 102

order of operations for propositions

1) ¬(not) 2) ^ (and) 3) v (or)

Indicate which statements are propositions: 1. 10 is a prime number 2. shut the door 3. All politicians are dishonest 4. Would you like some cake? 5. Interest rates will rise this year

1. Proposition 2. Not a proposition (a command) 3. Proposition (matter of opinion) 4. not a prop (it is a question) 5.Proposition

Indicate whether each statement is true or false. In each case, use the inclusive OR. 1. 4 is an even number or 4 is a prime number 2. 5 is a prime number or 3 is a prime number 3. 2 is a negative number or -3 is a positive number

1. True (since at least 1 of the 2 statements are true, it is true) 2. True (since both statements are true, the whole thing is true) 3. False (since both statements are false, the statement is false)

^

and

inverse

when both propositions in a conditional proposition are negated

contradiction

when in a compound proposition, the proposition is always false, regardless of the truth value of the individual propositions

tautology

when the proposition in a compound proposition is always true regardless of the individual propositions within it

converse

when the values for the hypothesis and conclusion are opposite

If there are 3 variables in a compound proposition, how many rows will there be?

8

Propositions vs non-propositions

Prop: typically declarative sentences, either true or false Non- prop: questions, commands

conditional proposition

a compound proposition that uses a conditional operation

proposition

a statement that is either true or false

truth value

a value indicating whether the proposition is actually true or false. The truth value can be true, false, unknown, or matter of opinion

negation operation

acts on just one proposition and has the effect of reversing the truth value of the proposition

conditional statement

another name for a conditional proposition

logical operation

combines propositions using a particular composition rule

compound propositions

created by connecting individual propositions with logical operations

conditional operation

denoted with the symbol -> ; means if p then q. The proposition is always true unless p is true and q is false

inclusive or

evaluates to true when one or both of the propositions (p or q) are true. The inclusive or is the most common in logic and is called "or" for short

exclusive or

evaluates to true when p is true and q is false or vice versa

logically equivalent

if two compound propositions have the same truth values regardless of the individual propositions

iff

means 'if and only if'

v

or

p^q

read as "p and q"; both must be true for the proposition to be true

pvq

read as "p or q"; only one has to be true for the proposition to be true

logic

the study of formal thinking

biconditional operation

true when both propositions are true and false when both propositions have different truth values; denoted by <->

contrapositive

when both propositions from a conditional statement are negated and converse