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Affirming the Consequent

A free Logic lesson from the “Argument Validity” unit, with a worked example and practice problems including step-by-step solutions.

Affirming the consequent confuses a sufficient condition with a necessary one. A conclusion may happen for more than one reason. Learning objective: Recognize why p → q, q, therefore p is invalid. Prerequisite: No formal prerequisite. Work in this lesson starts with ordinary language, then connects the idea to symbols only after the meaning is clear. Example 1: 'If p then q; p; therefore q' is valid modus ponens. Example 2: 'If p then q; q; therefore p' is affirming the consequent and is invalid. A common misconception is to treat familiar wording as proof; instead, check exactly what the statement says and what follows from it.

What you'll learn

Why it matters: Argument validity helps learners spot reasoning errors in word problems, explanations, and public claims.

Worked example

Problem. Example case A (Affirming the Consequent): Worked example: If it rains, then the field is wet. The field is wet. What is the correct logical assessment?

  1. Worked Example: First identify exactly what the question is asking: Example case A (Affirming the Consequent): Worked example: If it rains, then the field is wet. The field is wet. What is the correct logical assessment?
  2. Compare each choice with the stated logical rule, and eliminate choices that change the claim's meaning.
  3. Affirming the consequent uses p -> q and q.
  4. q might be true for another reason.

Answer: Invalid: something else could have made the field wet.

Practice problems

1. Practice case A (Affirming the Consequent): Practice: If it rains, then the field is wet. The field is wet. What is the correct logical assessment?

Choices: Invalid: something else could have made the field wet. · Valid: it must have rained. · Valid: this is modus tollens. · Invalid only because the statements use words.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Practice case A (Affirming the Consequent): Practice: If it rains, then the field is wet. The field is wet. What is the correct logical assessment?
  2. Compare each choice with the stated logical rule, and eliminate choices that change the claim's meaning.
  3. Affirming the consequent uses p -> q and q.
  4. q might be true for another reason.
  5. Therefore p does not have to follow.
  6. Verify the selected choice by checking that it preserves the stated logical meaning and that the other choices change the rule or claim.

Answer: Invalid: something else could have made the field wet.

2. Practice case B (Affirming the Consequent): Practice: Which argument form does this use? "If a figure is a square, then it has four sides. This figure has four sides."

Choices: Affirming the Consequent · Modus Ponens · Modus Tollens · Hypothetical Syllogism

Show solution
  1. Affirming the Consequent has the pattern p -> q; q; therefore p.
  2. Match the premises and conclusion to the pattern.
  3. This form is a common invalid look-alike.

Answer: Affirming the Consequent

3. Practice case C (Affirming the Consequent): Practice: Which symbolic pattern names Affirming the Consequent?

Choices: p -> q; q; therefore p · p -> q; p; therefore q · p -> q; ¬q; therefore ¬p · p -> q; q -> r; therefore p -> r

Show solution
  1. Warm-up: First identify exactly what the question is asking: Practice case C (Affirming the Consequent): Practice: Which symbolic pattern names Affirming the Consequent?
  2. Compare each choice with the stated logical rule, and eliminate choices that change the claim's meaning.
  3. Affirming the Consequent has a specific shape.
  4. p -> q; q; therefore p
  5. This form is a common invalid look-alike.
  6. Verify the selected choice by checking that it preserves the stated logical meaning and that the other choices change the rule or claim.

Answer: p -> q; q; therefore p

4. Practice case D (Affirming the Consequent): Practice: Is Affirming the Consequent a valid argument form?

Choices: Invalid: the conclusion does not have to follow. · Valid: the conclusion must follow from the premises. · It depends only on whether the conclusion sounds realistic. · It is valid only when the sentences use variables.

Show solution
  1. Affirming the Consequent is a tempting but invalid form.
  2. Affirming the consequent uses p -> q and q.
  3. q might be true for another reason.

Answer: Invalid: the conclusion does not have to follow.

5. Practice case E (Affirming the Consequent): Practice: Why is Affirming the Consequent invalid?

Choices: q can be true for another reason, so p does not have to hold. · Because the sentences are too long. · Because it uses symbols. · Because the conclusion sounds false.

Show solution
  1. Invalid means the conclusion can fail while premises hold.
  2. q can be true for another reason, so p does not have to hold.
  3. So the conclusion is not guaranteed.

Answer: q can be true for another reason, so p does not have to hold.

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