Question

What law can be used to determine that the conclusion is valid based on the given statements

Given: if angle is acute the it cannot be obtuse. A is acute

Conclusion: A cannot be obtuse

A. Law of detachment

B. Law of syllogism

C. Law of converse

D. The conclusion is not valid

Answer 1

The valid conclusion that 'A cannot be obtuse' given that 'A is acute' and 'if an angle is acute then it cannot be obtuse' is determined by the Law of Detachment in deductive reasoning.

Step-by-step explanation:

The law that can be used to determine that the conclusion is valid based on the given statements, which are "if an angle is acute then it cannot be obtuse" and "A is acute", is the Law of Detachment. The Law of Detachment allows us to infer the conclusion that "A cannot be obtuse" directly from the given conditional statement and the fact that A meets the condition of being acute. This is a simple form of modus ponens, where we affirm the antecedent (A is acute) and, therefore, can also affirm the consequent (A cannot be obtuse). This deductive reasoning method fits the definition of valid since if the premises are true, the conclusion necessarily must be true.

Answer 2

A. Law of detachment

Step-by-step explanation:

The Law of detachment implies that when one condition is fulfilled the other cannot be and vice versa, then it is made the conclusion.

This condition is made the conclusion.

The Acute and Obtuse are detached of each other.

The acute angle is one in which the value of the angle is less than 90 degrees and obtuse angle is one in which the angle is greater than 90 degrees but less than 180 degrees.

Thus angles less than 90 degrees are acute and greater than 90 degrees are obtuse.

The conclusion of the given statement is valid based on the law of detachment as the condition has been made a conclusion.