Deductive Reasoning Flashcards
deductive argument
A valid deductive argument with only true premises must have a true conclusion. An argument presented as deductive is flawed if its premises can all be true while its conclusion is false. However, a flawed deductive argument might still work well as an inductive argument if the author doesn’t wrongly present the premises as proving the conclusion.
logical operator
Shows how the truth or falsehood of one or more statements affect the truth or falsehood of a larger statement made from them and the operator.
basic logical operators
negations, logical conjunctions, disjunctions, and implications
negation
is true just when the statement is false. Words and phrases like not, it is false that, and it is not the case that often mark negation.
logical conjunction of two statements
is true just when both are true
disjunction of two statements
is true only when one of them is true
inclusive disjunction
true when at least one of them is true, and also when both are
exclusive disjunction
true just when exactly one of them is true—not when both are
conditional
for one statement to be true, another must be true
logically equivalent statements
are always both true or both false under the same conditions
not (A and B)
not-A or not-B
not (A or B)
not-A and not-B
if A then B
if not-B then not-A
if A then (B and C)
(if A then B) and (if A then C)
if A then (B or C)
(if A then B) or (if A then C)
if (A or B) then C
(if A then C) and (if B then C)
necessarily true
there’s a 100 percent chance the statement is true
probably true
there’s a good chance the statement is true
possibly true
the odds are greater than 0 percent that the statement is true
quantifier
a word or phrase for a proportion, number, or amount
All As are Bs
No As are not Bs
Some As are not Bs
Not all As are Bs
syllogism
a type of simple argument whose two premises have one quantifier apiece, and whose conclusion also has one quantifier.
