statements p and q are given below. p = the angle is obtuse. q = the measure of an angle is 98°. which…
statements p and q are given below. p = the angle is obtuse. q = the measure of an angle is 98°. which conditional statement is logically equivalent to the following statement? if the measure of an angle is 98°, then the angle is obtuse? ~q→~p p→q ~p→q ~p→~q
Answer
Explanation:
Step1: Recall logical equivalence
A conditional statement (A\rightarrow B) is logically equivalent to its contra - positive (\neg B\rightarrow\neg A).
Step2: Identify the original statement
The original statement is (Q\rightarrow P) where (Q) is "The measure of an angle is (98^{\circ})" and (P) is "The angle is obtuse".
Step3: Find the contra - positive
The contra - positive of (Q\rightarrow P) is (\neg P\rightarrow\neg Q).
Answer:
(\neg P\rightarrow\neg Q)