if A, then B
A
Therefore B
modus ponens (mp)
valid
If A then B
Not B
Then Not A
modus tollens (mt)
valid
If A then B
If B then C
Therefore if A then C
Hypothetical Syllogism (hs)
valid
Either A or B
not A
Therefore, B
Disjunctive Syllogism (ds)
valid
Either A or B
not B
therefore A
Disjunctive Syllogism (ds)
valid
either A or B
If A then R
If B then S
Therefore, either R or S
Constructive Dilemma (cs)
valid
If A then B
Not A
Therefore not B
fallacy of denying antecedent (invalid)
If A, then B
B
Therefore, A
fallacy if affirming consequent (invalid)
Logical Constants (5x)
Not, And, Or, If-Then
Atomic Statement
one that does not have any other statement as a component (No logical words, operating as logical constants)
Compound Statement
one that has at least one atomic statement as a component
3 Important pieces to MEMORIZE
- symbolize “unless” with V
- Antecedent always comes after “if”, except in the case of “Only if” (then the consequent comes after)
- Antecedent= sufficient condition
Consequent= necessary condition
Antecedent
The If-clause of a conditional
Consequent
The Then-clause of a conditional
Examples of Not (tilde/negation)
not the case, isn’t, it is false that, fails to be, it isn’t true that, etc.
Examples of And (dot/conjunction)
but, however, while, although, even though
Examples of Or (vee/disjunction)
unless, either, and/or
inclusive: either, or both
exclusive: either or but NOT both
Main logical operator
governs largest component(s)
-most control
Examples of “If” and “Only If”
Just in case, is necessary and sufficient condition
Disjunction
An either-or statement
(components are called disjuncts)
Conditional statement
an if-then statement
A is sufficient for B
A arrow B
A if B
B arrow A
A ONLY IF B
A arrow B
