Question

Use the premises and conclusion to answer the questions. Premises: If an angle measure is less than 90°, then the angle is an acute angle. The measure of angle ∠B is 48°. Conclusion: ∠B is an acute angle. Is the argument valid? Why or why not? The argument is not valid because the conclusion does not follow from the premises. The argument is not valid because the premises are not true. The argument is valid by the law of syllogism. The argument is valid by the law of detachment.

Answer 1

The law of detachment states the following:

If p and q are 2 propositions (or statements, or assertions) then,

Statement 1: If p, then q.
Statement 2: p
Conclusion: q

That is, if q follows from p, and if p is true, then q is true.


Statement 1: If angle ∠B measure is less than 90°, then ∠B is an acute angle.
Statement 2: The measure of angle ∠B is 48°

Conclusion: ∠B is an acute angle


Answer: The argument is valid by the law of detachment.