Question

select the term that best describes the statement. a triangle is obtuse provided all the angles have a measure greater than 90 degrees. ○ conjunction ○ conditional ○ disjunction ○ negation

Explanation:

1. First, recall the definitions:

• A conjunction is a statement of the form \( p \land q \) (both \( p \) and \( q \) are true).
• A conditional is a statement of the form \( p \to q \) (if \( p \), then \( q \); or \( q \) provided \( p \)).
• A disjunction is a statement of the form \( p \lor q \) (either \( p \) or \( q \) is true).
• A negation is a statement of the form \(

eg p \) (not \( p \)).

1. The given statement is "A triangle is obtuse provided all the angles have a measure greater than 90 degrees". In logical terms, "provided" means "if", so we can rephrase it as "If all the angles of a triangle have a measure greater than 90 degrees, then the triangle is obtuse". This fits the form of a conditional statement \( p \to q \), where \( p \) is "all the angles have a measure greater than 90 degrees" and \( q \) is "a triangle is obtuse".

• It is not a conjunction because it is not asserting two statements are both true.
• It is not a disjunction because it is not asserting either of two statements is true.
• It is not a negation because it is not denying a statement.

Answer:

B. conditional