Symbols
~
Negation
~(A∨B)⊃C
⊃
If everything is perfect, then I can’t be blamed for me mistakes.
~E⊃~B
An argument where it’s possible to have all true premises and a false conclusion.
Valid Argument
A sentence whose logical form guarantees that it’s always true
Tautology
∨
Disjunction
~[~(A∨B)⊃C]
The first tilde
If the extinction of dinosaurs was not caused by a meteor, the spread of disease did it.
~M⊃D
If a set of statements can be true at the same time.
Consistent
A sentence whose logical form guarantees that it’s always false
Self-Contradiction
·
Conjunction
~[(A∨B)⊃C]⊃D
The second horseshoe
You Missed you appointment and the boss is not happy, but it’s not my fault.
(M·~H)·~F
A statement that cannot logically interpreted any other way is called _______.
A well-formed formula
A statement whose one-one form has at least one T and one F in the truth tables.
Contingent statement
⊃
Conditional
[~A∨(B⊃C)]≡~D
Tribar ≡
Bob will not win the election unless a miracle happens, yet he is the best candidate.
(~M⊃~W)·B
A sentence p is said to logically imply q iff p≡q is a tautology, thus giving them the same truth values on each line of the truth table.
Logically equivalent
A sentence obtained by a sentence form by replacing all the sentence variables in the sentence form by sentences, making sure that every occurrence of a given sentence variable is replaced by the same sentence.
Substitution Instance
≡
Biconditional
[(~A⊃B)∨C]≡~(D·R)
≡
Neither rain nor snow nor gloom of night will prevent your postal carrier from delivering the mail.
[(R∨S)∨G],
OR
(~R·~S)·~G
The set consisting of the premises of an argument and the denial of the argument’s conclusion. An argument is said to be valid iff this is inconsistent.
Counterexample Set
A method of determining the truth-value of a sentence from knowledge of the truth-values of its component sentences.
Truth Table analysis