Consider the following statements:
m = Edna is respectful
n = Edna is brilliant,
If m ⇒ n, which of the following is valid?
A
¬n ⇒ ¬m.
B
¬m ⇒ ¬n.
C
n ⇒ ¬m.
D
m ⇒ n.
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Given: m: Edna is respectful, n: Edna is brilliant
From the implication m ⇒ n:
a) Contra-positive: If Edna is not brilliant (¬n), then she is not respectful (¬m): ¬n ⇒ ¬m
b) Direct: If Edna is respectful (m), then she is brilliant (n)
c) Invalid: If Edna is brilliant (n), we cannot conclude she is respectful (m)
Thus, the valid conclusion is: ¬n ⇒ ¬m.
Source: Myschool Past Questions Archive (Record #71778)