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