Logical statement

Definition

A logical statement is a declarative sentence that is either true or false but not both. It forms the basic building block of logical reasoning and propositions.

5 Must Know Facts For Your Next Test

1. Logical statements are essential for constructing arguments and proofs.
2. The truth value of a logical statement can be either true (T) or false (F).
3. Logical operators such as AND, OR, and NOT are used to combine or modify logical statements.
4. Quantifiers like 'for all' (∀) and 'there exists' (∃) specify the scope of a logical statement in mathematical logic.
5. Compound statements are formed by combining multiple logical statements using logical connectives.

Review Questions

• What is the truth value of a logical statement?
• Name three common logical operators used in forming compound statements.
• How do quantifiers affect the meaning of a logical statement?

Related terms

Proposition:

A proposition is another term for a logical statement; it asserts something about a subject.

Quantifier:

'Quantifier' specifies the scope of variables in a statement, such as 'for all' (∀) or 'there exists' (∃).

Logical Connective: 'Logical connective' refers to symbols or words like AND, OR, NOT that combine or modify statements to form compound ones.