Question

unit 2 test
willhite_k_geometry a_section 1_fall 25/26 / unit 2 - logic and proofs
the part of a conditional statement that expresses the conditions that must be met by the statement is called the

hypothesis

conclusion

conditional statement

conjunction

1. choose the best answer.

is this a valid argument?
given: if a closed geometric shape has three sides, then it is a triangle.
closed geometric shape abc has three sides.
conclusion: shape abc is a triangle

yes. this argument uses the law of syllogism.

no. this is an improper use of the law of syllogism.

yes. this argument uses the law of detachment.

Explanation:

A conditional statement is in the form "If \(p\) (hypothesis), then \(q\) (conclusion)". The hypothesis is the condition. For the argument, the Law of Detachment states that if \(p
ightarrow q\) (if a closed - geometric shape has three sides (\(p\)), then it is a triangle (\(q\))) and \(p\) (closed geometric shape \(ABC\) has three sides), then \(q\) (shape \(ABC\) is a triangle).

Answer:

For the first question: hypothesis.
For the second question: Yes. This argument uses the Law of Detachment.