Set Theory: 1.3 Statements and Connecting Words

Vocabulary flashcards covering mathematical statements, negations, compound statements, and the truth conditions for logical connectives "and" and "or".

Statement

A sentence that is either true or false. For it to be considered a statement, it cannot have a maybe or sometimes factor.

Negation

The opposite of a statement.

Compound Statement

A statement formed by joining more than one statement using joining words such as "and" and "or".

Truth Condition for "And"

A compound statement joined by "and" is only true if both statements are true. Otherwise, it will be false.

Truth Condition for "Or" in Mathematics

A compound statement in the form "$A \text{ or } B$" means $A$ is true, $B$ is true, or both $A \text{ and } B$ are true.

Negation of "Some" Statements

A quantified statement negation that begins with "no" or "none" (for example, the negation of "Some mammals live in the ocean" is "No mammals live in the ocean").