Ch.7 Flashcards
Propositional logic
The branch of deductive reasoning that deals with logical relationships among statements.
•Statement: an assertion that some thing is or is not the case.
•Simple statement: statement containing no other statements as constituents.
-Frank is cold
•Compound statement: A statement composed of at least two simple statements.
-Frank is cold and Tom is warm 
Connective and truth values:
Symbols, meaning, and examples
Symbol- &
Meaning- Conjunction (and)
Ex- p & q. Alice rode her bike, and John walked.
Symbol- v
Meaning- Disjunction (or)
Ex- p v q. Either Alice rode her bike or John walked.
Symbol- ~
Meaning- Negation (not)
Ex- ~p. Alice did not ride her bike. (Or) It is not the case that Alice rode her bike.
Symbol- —>
Meaning- Conditional (if-then)
Ex- p —> q. If Alice rode her bike, then John walked.
Truth tables
Conjunction p q p & q
T T T
T F F
F T F
F F F
Negation p ~p
T F
F T
Disjunction p q p v q
T T T
T F T
F T T
F F F
Conditional p q p —> q
T T T
T F F
F T T
F F T
Either you go to the mall this weekend, or you won’t
•The statement seems true
•Our truth table tells us, if a disjunction is true, one of it’s disjuncts must be true.
•But If one of them is already true in the future must be set.
•so the future is set. everything you do is faithed and you have no free will (BTW). 
Aristotle’s response
•Statements about the future are neither true nor false.
•They become true or false once events happened.
•But then disjunctions about the future Are neither true nor false?
• but either you will go to the mall, or you won’t, right?
•How could ir not already be true?
Conditionals
•The truth table for conditionals might seem counterintuitive.
•but a conditional is only asserting that if p is true, q must be true.
•It’s not saying that P is in fact true
•So it’s only false when the Antecedent is true but the conditional is false.
•Other rows, could still be true, so the conditional not proven false
Conditionals are not always expressed in the standard if-then configuration
•Only if: introduces the consequent.
(q = p —> q)
- I’ll ride the bus only if I’m late
- If I ride the bus, then I’m late
•Provided: introduces the antecedent.
(q = q —> p)
-Gregory will excel in school provided that he studies hard.
-If Gregory studies hard then he will exceed in school.
•Unless: introduces the antecedent
(q = ~q —> p)
-I will walk the dog unless it’s raining.
-If it’s not raining, I will walk the dog.
•Whenever: introduces the antecedent.
( q = p —> q)
-Whenever I think, I get a headache.
-If I think, I get a headache. 
The truth table test of validity
•It’s impossible for a valid argument to have true premises and a false conclusion.
•If any truth table row shows true premises and a false conclusion, the argument is invalid.
If the iceberg melts, the low lands will flood.
The icebergs will not melt.
Therefore, the low lands will not flood.
p —> q. (If the iceberg melts, the low lands will flood.)
~p (The icebergs will not melt.)
~q (Therefore, the low lands will not flood.)
Invalid (Denying the antecedent)
Either we fight or give into Tyranny
We won’t fight.
Therefore, we will give into Tyranny.
p v q. (Either we fight or be given to Tyranny)
~p (We won’t fight.)
q (Therefore, we will give them to Tyranny.)
Valid (Disjunctive syllogism)
Common argument forms symbolized
Modus ponens (valid)
p —> q
p
Therefore q
Modus tollens (valid)
p —> q
~q
Therefore ~p
Hypothetical syllogism (valid)
P —> q
q —> r
Therefore p —> r
Disjunctive syllogism (valid)
p v q
~p
Therefore q
Denying the antecedent (invalid)
P —> q
~p
Therefore ~q
Affirming the consequent (invalid)
P —> q
q
Therefore p
