Question

given this conditional statement, assess the validity of its related conditionals. if < a = 15°, then < a is acute. the conditional statement is. the converse is. the inverse is. the contrapositive is. the biconditional for this statement would be

Explanation:

Step1: Define an acute - angle

An acute angle is an angle whose measure is between 0° and 90°. Since 15° is between 0° and 90°, the conditional statement "If ∠A = 15°, then ∠A is acute" is true.

Step2: Find the converse

The converse of "If p, then q" is "If q, then p". Here, the converse is "If ∠A is acute, then ∠A = 15°". An acute angle can have many measures (e.g., 30°, 45°), so the converse is false.

Step3: Find the inverse

The inverse of "If p, then q" is "If not p, then not q". The inverse is "If ∠A≠15°, then ∠A is not acute". There are many non - 15° angles that are acute (like 30°), so the inverse is false.

Step4: Find the contrapositive

The contrapositive of "If p, then q" is "If not q, then not p". The contrapositive is "If ∠A is not acute, then ∠A≠15°". If an angle is not acute (i.e., ∠A≥90° or ∠A≤0°), then it is not 15°, so the contrapositive is true.

Step5: Find the biconditional

The biconditional "p if and only if q" is true when both the conditional and its converse are true. Since the converse is false, the biconditional "∠A = 15° if and only if ∠A is acute" is false.

Answer:

The conditional statement is True. The converse is False. The inverse is False. The contrapositive is True. The biconditional for this statement would be False.