WAEC - Mathematics (2024 - No. 16)

Consider the following statements:

m = Edna is respectful

n = Edna is brilliant,

If m ⇒ n, which of the following is valid? 

¬n ⇒ ¬m.
¬m ⇒ ¬n.
n ⇒ ¬m.
m ⇒ n.

Explanation

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.

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