Introduction to Logic Exam 1

Argument

A series of claims, one of which, called the conclusion, is supported by others, called the premises.

Inductive Logic

Logic that concerns arguments that move from particular claims to general ones. It yields probable conclusions.

Deductive Logic

Logic that concerns arguments that move from general claims to particular ones. It yields certain conclusions.

Valid

An argument is ______ if and only if it is impossible for the conclusion to be proven false provided that the premises are true. An argument is also _____ if the premises logically imply or entail the conclusion. If the argument is not _____, we can find a counter example.

Sound

An argument is _____ if and only if the argument is valid and the premises of the argument are actually true.

Compound sentence

A sentence that contains another sentence as a component (or it can be rephrased more fully to display that it literally contains another sentence as a distinctive component) and the remaining words can be joined with any sentences to form a sensible new sentence.

Simple sentence

A sentence that is not compound.

Counter Example

An example in which all the premises are true but the conclusion is false. It shows that the argument isn’t valid.

Negation

True if and only if the truth value of the initial statement is false.

Conjunction

True if and only if both components are true

Disjunction

True if and only if at least one of the statements is true

Conditional

False if and only if the antecedent is true and the consequent is false

Biconditional

True if and only if both statements are true OR both statements are false

Conjunction ●

And, but, yet, however, nevertheless, though, although, in addition, moreover, furthermore, despite, and ;

Disjunction ∨

or, unless, either…or

Negation ~

not, it is not the case that, no

Conditional ⊃

If…then, if, provided, provided that, supposing

Biconditional ☰

If and only if, just in case, exactly when

Tautology

A statement where the values are always true

Contradiction

A statement where the values are always false

Contingency

A statement that has both true and false truth values

Logical Implication

A statement _____ _____ another statement if and only if there is no row in their joint truth table where the first is true and the second is false.

Logical equivalence

Two statements are ______ ______ if and only if the two statement forms have the same truth values in every row of their truth table.