Thinking Critically: Propositions and Truth Values 1b

Flashcards covering key concepts from the lecture notes on propositions, truth values, negations, logical connectors, conjunctions, disjunctions, conditional statements, and logical equivalence.

What is a proposition?

A proposition makes a claim (either an assertion or a denial) that may be either true or false. It must have the structure of a complete sentence.

What are the possible truth values for any proposition?

T = true or F = false.

What is a truth table?

A table with a row for each possible set of truth values for the propositions being considered.

What is the negation of a proposition?

Another proposition that makes the opposite claim of p. If p is true (T), not p is false (F). If p is false (F), not p is true (T).

What is the symbol for negation?

~

What is a double negation?

The double negation of a proposition p, not not p, has the same truth value as p.

What are logical connectors?

Words such as and, or, and if…then that join propositions.

What is a conjunction?

Given two propositions p and q, the statement p and q is called their conjunction. It is true only if p and q are both true.

What is the logic of 'or'?

In logic, assume 'or' is inclusive unless told otherwise, meaning 'either or both.'

What is a disjunction?

Given two propositions p and q, the statement p or q is called their disjunction. It is true unless p and q are both false.

What is a conditional proposition (or implication)?

A statement of the form if p, then q. It is true unless p is true and q is false.

In 'if p, then q', what are p and q called?

p is called the hypothesis, and q is called the conclusion.

What are the variations on the conditional?

Converse: If q, then p. Inverse: If not p, then not q. Contrapositive: If not q, then not p.

What does it mean for two statements to be logically equivalent?

They share the same truth values.