1/9 1. Propositions and Truth Values Free Online FlashCards

What is a proposition?

A proposition is a declarative claim with one definite truth value: true or false.

What truth values does classical logic use?

Classical propositional logic uses two truth values: true, abbreviated T or represented by 1, and false, abbreviated F or represented by 0.

Must a proposition’s truth value be known?

Yes. A sentence can be a proposition even when its truth value is currently unknown, as long as it makes one definite claim.

Is “Is the library open?” a proposition?

No. A question does not assert a claim with a truth value, so it is not a proposition by itself.

What is an open sentence?

An open sentence has a truth value that depends on an unresolved variable, such as $x+2=5$. It becomes a proposition when a value is supplied or a quantifier binds the variable.

What is a simple proposition?

A simple, or atomic, proposition contains no smaller propositions joined by a logical connective.

What is a compound proposition?

A compound proposition combines one or more propositions using a logical connective such as “not,” “and,” “or,” “if ... then,” or “if and only if.”

How does “but” function logically?

In basic logical structure, “but” functions like “and,” so the statement is a conjunction of two component claims.

Why can “It is cold” lack one proposition?

A context-dependent sentence may fail to express one definite proposition until relevant details, such as place or time, are fixed.

What does a truth table show?

A truth table systematically lists possible truth values for component propositions and the resulting values of a compound proposition.

How many combinations come from $n$ independent propositions?

With $n$ independent propositions, a truth table has $2^n$ possible truth-value combinations.

When is $p\land q$ true?

The conjunction $p\land q$ is true only when both $p$ and $q$ are true.