L
Propositonal Logic
a branch of formal, deductive logic in which the basic unit of thought is the proposition
Proposition
a statement(a sentence with a truth value)
truth-functional proposition
a proposition whose truth value depends on the truth value of its component parts
compound proposition
a proposition with more than one component part or a modified (negated) part
logical operators
words which combine or modify simple propositions to make compound propositions
propositional constant
-upper case letter
-represents a single, given proposition
propositional variable
-lower case letter
-represents any proposition
Truth Table (tool#1)
a listing of possible truth values for a set of one or more propositions.
Defining Truth Table
a truth table that completely defines its operations on a minimum number of variables (shown in Appendix A)
negation
~ "not"
logical operator that denies or contradicts a proposition
conjunction
. "and"
logical operator that joins 2 propositions (disjuncts) and is true if and only if both propositions are true
disjunction
V "or"
logical operator that propositions (disjuncts) and is false if and only if both propositions are false
conditional
) "If...then..."
logical operator that asserts that one component part (the antecedent) implies the other (the consequent).
biconditional
"if and only if"
It is true when both parts have the same truth value, and false when their truth values are different.
Logical equivalence
Two propositions are logically equivalent if and only if they have identical truth values.
tautology
a proposition that is always true due to its logical structure. (every row of its truth table is true)
self-contradiction
a proposition that is always false due to its logical structure. (every row of its truth table is false)
valid argument
In a valid argument, if the premises are true, the conclusion must be true.
Assumed value in Shorter Truth Table Method for testing validity
Using a truth table when no more values can be determined with certainty.
Truth value of conclusion in a Shorter Truth Method for testing validity
False
antecedent
the proposition that follows the "if" in a conditional proposition
consequent
the proposition that follows the "then" in a conditional proposition
statement equivalent to p)q
If p then q
defining truth table
a truth table that completely defines its operations on a minimum number of variables.
truth value of premises in a Shorter Truth table Method for testing validity
True