Exam 1 Flashcards
Argument composed of 2 statements followed by a conclusion
Syllogism
An argument is__________ if the conclusion is guaranteed assuming the premises are true
Valid
An Argument is ___________ if the conclusions not guaranteed when the premises are true
Invalid
What is the symbol for negation (Not), the denial of a statement?
~
What is the symbol for Conjuctions, two or more statements connected with the word and?
What is the symbol for disjunctions 2 or more statements connected by the word or
V
What is the symbol for conditionals, any statement of the form (if p then q) or equivalent
->
All and None are secretly…
If Then Statements
The thing that is necessary is the
Then part
Ex. Let p=Karlene has to work tonight Let q=Karlene has homework tonight
Karlene has to work or do homework tonight
pVq
Ex. Let p=Karlene has to work tonight Let q=Karlene has homework tonight
Karlene has to work or has no homework tonight
pV~q
Ex. Let p=Karlene has to work tonight Let q=Karlene has homework tonight
Karlene has no work or she has homework tonight
~pVq
Ex. Let p=Karlene has to work tonight Let q=Karlene has homework tonight
Karlene has work and homework tonight or she has no work and no homework
(p^q)V(~p^~q)
Ex. Let p=Ester’s car has a flat tire, q=Ester takes the bus, r=Ester is late to class
If Ester’s car has a flat tire and she does not take the bus then, Ester is late for class
(p^~q)->r
Ex. Let p=Ester’s car has a flat tire, q=Ester takes the bus, r=Ester is late to class
If Ester’s car does not have a flat tire then she takes the bus or is late for class
(~p)->(qVr)
In a truth table, for a conjunction(and), p^q is only true if
p is true and q is true
In a truth table, a disjunction (or) pVq is only false if
p and q are false
In a truth table, a condition (if,then) p->q is only false if
p is true and q is false`
On a truth table with only p & q what is the pattern for p
T T F F
On a truth table with only p & q what is the pattern for q
T F T F
On a truth table with, p, q and r. What is the pattern for p
T T T T F F F F
On a truth table with p, q and r what is the pattern for q
T T F F T T F F
On a truth table with p, q and r What is the pattern for r
T F T F T F T F
If p=I am nice to you and q=You are my friend What is the symbolic for of this sentence?
If I am Nice to you then you are my friend
p->q
If p=I am nice to you and q=You are my friend What is the symbolic for of this sentence?
If you are my friend, then I am nice to you.
q->p
If p=I am nice to you and q=You are my friend What is the symbolic for of this sentence?
If I am not nice to you, then you are not my friend.
~p->~q
If p=I am nice to you and q=You are my friend What is the symbolic for of this sentence?
If you are not my friend, then I am not nice to you.
~q->~p
What is the converse of p->q
q->p
What is the inverse of p->q
~p->~q
What is the contrapositive of p->q
~q->~p
In Biconditionals p and only if q is equivalent to
p->q
Using Biconditionals, if and only if q is
p<->q
What is the other way you can write a Biconditional for p if and only if q
(p->q)^(q->p)
