Consider the following argument

Consider the following argument: If people always betray you, it is not worth cultivating friendships. But people do not always betray you. Therefore, it is indeed worth cultivating friendships. It is an instance of: a. Affirming the consequent b. Affirming the antecedent c. Denying the antecedent d. Denying the consequent

The correct answer and explanation is:

The correct answer is: d. Denying the consequent

Explanation:

Let’s analyze the argument step-by-step:

Argument:

1. If people always betray you, then it is not worth cultivating friendships.
   Symbolically:
   If P, then Q
   Where:
   • P = People always betray you
   • Q = It is not worth cultivating friendships
2. People do not always betray you.
   Symbolically:
   Not P
3. Therefore, it is worth cultivating friendships.
   Symbolically:
   Therefore, Not Q

Form of the argument:

• The argument states:
  If P → Q
  Not P
  Therefore, Not Q

Validity Check:

• This is a classic logical form known as Denying the Antecedent if the conclusion was Q, but here the conclusion is Not Q after Not P, so we need to be careful.

Actually, given the symbols:

• P = “People always betray you”
• Q = “It is not worth cultivating friendships”

Given: If P then Q
Given: Not P (people do not always betray you)
Conclusion: Therefore, Not Q (it is worth cultivating friendships)

This matches the pattern:
If P then Q
Not P
Therefore, Not Q

This is the fallacy of denying the antecedent.

Why is this a fallacy?

• The statement “If P then Q” tells us that whenever P is true, Q must be true.
• However, if P is false (Not P), it does not guarantee that Q is false.
• Q could be true or false independently when P is false.
• So, concluding Not Q from Not P is logically invalid.

But the answer choices are:

a. Affirming the consequent
b. Affirming the antecedent
c. Denying the antecedent
d. Denying the consequent

Which is it?

• Affirming the antecedent (valid):
  If P then Q
  P
  Therefore Q
• Affirming the consequent (fallacy):
  If P then Q
  Q
  Therefore P
• Denying the antecedent (fallacy):
  If P then Q
  Not P
  Therefore Not Q
• Denying the consequent (valid):
  If P then Q
  Not Q
  Therefore Not P

Our argument matches the Denying the antecedent form.

Final conclusion:

• The argument is an example of the fallacy of denying the antecedent, answer c.

Correction:

The correct answer is c. Denying the antecedent.

Summary:

The argument incorrectly assumes that because people do not always betray you (Not P), it must be worth cultivating friendships (Not Q). However, from the conditional “If P then Q,” the truth of Not P does not guarantee Not Q. This is a logical fallacy called denying the antecedent.