Statements and conditions

Recognize statements with a truth value and express the negation of a condition.

Meaning

A mathematical statement is a sentence that can be judged true or false. For a condition containing a variable, specify its domain and assign a value, or make a claim about all or some values, before judging truth.

Example

“7 is odd” is a true statement. For real “” is a condition: it is true at and false at Do not treat a subjective sentence with no defined criterion as a mathematical statement. Changing a variable's domain can change the truth of a statement.

Practice for this concept

Scope and references

Topics

Truth and falsity, conditions, negation of statements

Learning goal

Recognize statements with a truth value and express the negation of a condition.

Helpful background

Distinguish examples that satisfy a condition from those that do not.

Propositions and conditions

These choice exercises use specified finite sets, conditions, or proof steps. They do not establish constructing new counterexamples or proofs, or mastery of the whole logic area.

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