Intermediate Logic Vocab

Question 1

Propositional Logic and Propositions

Answer 1

A branch of formal, deductive logic in which the basic unit of thought is the proposition. A propostion is a statement.

Question 2

Truth functional propositions

Answer 2

A proposition is truth functional when its truth value depends upon the truth values of its component parts.

Question 3

Simple and Compound propositions

Answer 3

If a proposition has only one component part, it is a simple proposition. Otherwise, it is compound.

Question 4

Logical operators

Answer 4

Words which combine or modify simple propositions to make compound propositions.

Question 4

Logical operators

Answer 4

Words which combine or modify simple propositions to make compound propositions.

Question 5

Propositional constant

Answer 5

A uppercase letter that represents a single, given proposition.

Question 6

Propositional variable

Answer 6

A lowercase letter that represents any proposition.

Question 6

Propositional variable

Answer 6

A lowercase letter that represents any proposition.

Question 7

Negation (~, “not”)

Answer 7

Is the logical operator that denies or contradicts a proposition. Represents the words: not, it is false that, or any other phrase which denies or contradicts the proposition

Question 8

Truth table

Answer 8

A truth table is a listing of the possible truth values for a set of one or more propositions.

Question 9

Defining truth table

Answer 9

A defining truth table displays the truth values produced by a logical operator modifying a minimum number of variables.

Question 10

Conjunction (. , “and”)

Answer 10

Is a logical operator that joins two propositions and is true if and only if both the propositions (conjuncts are components of conjunction) are true. Represented by: and, but, still, or other similar words.

Question 11

Conditional operator (u,”if/then”)

Answer 11

Asserts that one component (the antecedent) implies the other (the consequent). It is false if and only if the antecedent is true and the consequent is false.

Question 11

Disjunction (v, “or”)

Answer 11

Is a logical operator that joins two propositions and is true if and only if one or both of the propositions (disjuncts are components of disjunction) is true. Understood in the inclusive sense of “or,” “this or that, or both.”

Question 12

Biconditional operator (=, “if and only if”)

Answer 12

Is true when both component propositions have the same truth value, and is false when their truth values differ.

Question 15

Logically equivalent

Answer 15

Two propositions are logically equivalent if and only if they have identical truth values.

Question 16

Tautology

Answer 16

A tautology is a proposition that is always true due to its logical structure.

Question 17

Self-contradiction

Answer 17

A self-contradiction is false by logical structure.

Question 18

Validity

Answer 18

In a Valid argument, if a premises is true, the conclusion must be true. If the premises can be true and the conclusion is false, then the argument is Invalid.