L

O

G

I

C

100

The logical operator that joins two propositions and is true if and only if both propositions are true.

What is a conjunction?

100

This is represented by a lower case letter and can represent any proposition.

What is PROPOSITIONAL VARIABLE?

100

Logical operator that denies or contradicts a proposition.

What is negation?

100

A statement.

What is a PROPOSITION?

100

A sentence which is either true or false

What is a statement?

200

What are 3 tools used in Propositional Logic?

1. Truth Tables

2. Formal Proofs

3. Truth Trees

200

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

What is a Truth Table?

200

A proposition with more than one component part or a modified (negated) part (MUST have at least 1 logical operator)

What is a COMPOUND PROPOSITION?

200

The proposition that follows the "if" in a conditional proposition.

What is the ANTECEDENT?

200

This is represented by an upper case letter, and represents a single, given proposition.

What is a PROPOSITIONAL CONSTANT?

300

The proposition that follows the "then" in a conditional proposition.

What is the CONSEQUENT?

300

The 3 main oppositions to escape the "horns of a dilemma"

1. Go between the horns.

2. grasp it by the horns

3. rebut the horns

300

This is a truth table that completely defines its operations on a minimum number of variables

What is a DEFINING TRUTH TABLE?

300

The logical operator that joins two propositions and is false if and only if both propositions are false.

What is a disjunction?

300

A proposition whose truth value depends on the truth value of its component parts.

What is a truth-functional proposition?

400

This is a proposition that is always true due to its logical structure

What is a tautology?

400

What are five statements that are equivalent to

- if p then q

- p implies q

- p only if q

- when p, q

- p is sufficient for q

400

Two propositions are considered THIS if and only if they have identical truth values.

What is LOGICALLY EQUIVALENT?

400

Valid argument forms which can be used to justify steps in a proof.

Rules of Inference

400

This is what we call words which combine or modify simple propositions to make compound propositions.

What are LOGICAL OPERATORS?

500

The steps for which are:

1. write premises in symbols and number them.

2. deduce intermediate conclusions using the rules of inference, justifying each step by writing the steps used as premises and the abbreviation for the rule.

3. continue until the desired conclusion is reached

What is the Formal Proof Method for validity?

500

A step-by-step deduction of a conclusion from a set of premises, each step being justified by an appropriate basic rule.

Formal Proof for Validity (tool #2)

500

A valid argument which presents a choice between two conditionals

What is a dilemma?

500

Construct a counter-dilemma using the same or similar components as the original dilemma - another way of looking at the facts in order to arrive at a different conclusion.

Rebut the Horns

500

What are two statements that are equivalent to

- p if q

- p is necessary for q

600

This is when a proposition is always false due to its logical structure.

What is self-contradiction?

600

In this type of argument, if the premises are true, the conclusion must be true.

What is a valid argument?

600

Reject at least one of the two conditionals in the conjunctive premise

Grasp the Horns

600

This is also called an extended, or double, Modus Ponens.

What is Constructive Dilemma

600

Provide a 3rd alternative (deny the disjunctive premise)

Go Between the Horns

700

This is called an extended, or double, Modus Tollens.

What is Destructive Dilemma

700

A proposition with only one component part (NO logical operators)

What is a SIMPLE PROPOSITION?

700

a set of propositions which CAN all be true at the same time.

consistent propositions

700

A branch of formal, deductive logic in which the basic unit of thought is the proposition

What is PROPOSITIONAL LOGIC?

700

A shorter truth table can test for these 3 relationships between propositions.

1. validity

2. consistency

3. equivalence

Click to zoom