Logic Exam Flashcards
Use logic to be logical
What does the symbol “ ^ “ mean
AND
What does the symbol “ v “ mean
OR
What does the symbol “ ¬ “ mean
NOT
What does the symbol “ —-> “ mean
IMPLIES
What does the symbol “ “ mean
IMPLIES (BOTH WAYS)
What does the symbol “ ∴ “ mean
Therefor
What does the symbol “ ≡ “ mean
Equivalent to
What is the first priority of the truth table
Parenthesis
What is the second priority of the truth table
Nots
What is the third priority of the truth table
Ands
What is the fourth priority of the truth table
Ors
How would you approach filling the truth table values for P if there are only 2 variables:
P alternates every 2 values.
ex: T T F F
How would you approach filling the truth table values for Q if there are only 2 variables
Q alternates every 1 value
ex: T F T F
How would you approach filling the truth table values for p if there are 3 variables
P alternates every 4 values
ex: T T T T F F F F
How would you approach filling the truth table values for q if there are 3 variables
Q alternates every 2 values
ex: T T F F T T F F
How would you approach filling the truth table values for r if there are 3 variables
R alternates every 1 values
ex: T F T F T F T F
How would you approach solving proofs
Start with most complicated side first
What do you do if you see an “ Or “
If there is one thing thats true then it is all true
What do you do if you see an “ And “
If there is one thing that is false then it is all false
What is a tautology
A formula that is true in every interpretation
What does “ Ǝ “ mean
At least one (there exists)
What does “ ∀ “ mean
For all (everyone)
Solve this:
~(~P) ≡
P
Solve this:
P v ~P ≡
True
Solve this:
P ^ ~P ≡
False
Solve this:
P v T ≡
True
Solve this:
P v F ≡
P
Solve this:
P ^ T ≡
P
Solve this:
P ^ F ≡
False
What is this law: (P v Q) ≡ Q v P
Commutative Law
What is this law: P v (Q v R) ≡ (P v Q) v R
Associative Law
What is this law: P ^ (Q v R) ≡ (P ^ Q) v (P ^ R)
Distributive Law
What is this law: ~(P v Q) ≡ ~P ^ ~Q
Demorgan’s Law
What is the law: P -> Q ≡ ~P v Q
Equivalent to the Conditional
What is the law: P Q ≡ (P -> Q) ^ (Q -> P)
Biconditional
What is the law: (Q ^ P) ≡ P ^ Q
Commutative law
What is the law: P ^ (Q ^ R) ≡ (P ^ Q) ^ R
Associative Law
What is the law: P v (Q ^ R) ≡ (P v Q) ^ (P v R)
Distributive Law
What is the law: ~(P ^ Q) ≡ ~P v ~Q
Demorgans law
In related statements, what is the original equivalent to
The contrapositive
(In related statements), what is p –> q called
Direct Statement
(In related statements), what is q –> p called
Converse
(In related statements), ~p –> ~q called
The inverse
How do you take the inverse of something
You negate both sides
(In related statements), ~q –> ~p called
Contrapositive
How do you take the contrapositive of something
Turn it around and negate both
When is p –> q = false
Only when p is true and q is false
When is p–> q = true
Only when p is false or q is true
What is step 1 of the transitive rule
Pick something that appears only once
What is step 2 of the transitive rule
Start with ending “one” of last equation
What is step 3 of the transitive rule
Pick the first and last value
What is the equation of modus ponens
p —> q
p_____
∴ q
What is the equation of modus tollens
p –> q
~q____
∴ ~p
What is the equation of disjunctive sylloquism
p v q
~p___
∴ q
What is the equation of transitive law
p –> q
q–>r
∴ p –> r
What equation is this:
p —> q
p_____
∴ q
Modus ponens
What equation is this:
p v q
~p___
∴ q
disjunctive sylloquism
What equation is this:
p –> q
~q____
∴ ~p
modus tollens
What equation is this:
p –> q
q–>r
∴ p –> r
transitive law
What is a tip to memorize a TRUE logical property
There are 2 of them. Both use OR. One of the two has a NOT.
What is a tip to memorize a FALSE logical property
There are 2 of them. Both use AND. One of the two has a NOT.
What ia a tip to memorize a P logical property
There are 3 of them. One uses AND. One uses OR. The other uses NOT.
What are some tips to memorize Demorgan’s Law
Contains NOT, (), P and Q
Two variations of the equation: OR x1 and AND x1
What effect does using Demorgan’s Law have on a statement
You distribute the sign throughout the parenthesis
(removing the parenthesis in the process) and flip the sign
What are some tips to memorize Communitative Laws
Contains (), P and Q
Two variations of the equation: OR x1 and AND x1
What effect does using the Communitative law have on a statement
Rearranges the statement so P is in the first place and parenthesis are removed
What are some tips to memorize Distributive Laws
Contains (), P, Q and R
What is special about both variations of the distributive laws
Both contain a sign outside that is different from inside the parenthesis
What are the signs in the first variation of the distributive law
and then (OR)
What are the signs in the second variation of the distributive law
or then (AND)
What effect does using the Distributive law have on a statement
Keep sign attached to P
outside the parenthesis) for inside the parenthesis. Then, inside sign goes inbetween the two () (
What are some tips to memorize Associative laws
Contains (), P, Q and R.
Two variations: OR x1, AND x1
What effect does using the Associative law have on a statement
Remove P from outside bracket, put into first spot in bracket. Shift original first value to second bracket position. Original last value in bracket goes outside the parenthesis
What are the tips to remember modus ponens
Contains p (implies) q
Second line is p
Therefore q
What are tips to remember modus tollens
Contains p (implies) q
Second line is not q
Therefore ~p
What are some tips to remember disjunctive sylloquism
Contains p (or) q.
Second line is ~p
Therefore q
What is a tip to memorize transitive law
Contains p (implies) q Second line is q (implies) r Therefor p (implies) r
