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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): Name the form: If p then q. p. Therefore q.

  1. Worked Example: First identify exactly what the question is asking: Example case A (Affirming the Consequent): Name the form: If p then q. p. Therefore q.
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. The argument uses p → q.
  4. It affirms p.

Answer: Modus ponens

Practice problems

1. Practice case A (Affirming the Consequent): Name the form: If p then q. p. Therefore q.

Choices: Modus ponens · Modus tollens · Affirming the consequent · Denying the antecedent

Show solution
  1. Warm-up: First identify exactly what the question is asking: Practice case A (Affirming the Consequent): Name the form: If p then q. p. Therefore q.
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. The argument uses p → q.
  4. It affirms p.
  5. Therefore q follows by modus ponens.
  6. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: Modus ponens

2. Practice case B (Affirming the Consequent): Name the form: If p then q. Not q. Therefore not p.

Choices: Modus tollens · Modus ponens · Affirming the consequent · Hypothetical syllogism

Show solution
  1. Warm-up: First identify exactly what the question is asking: Practice case B (Affirming the Consequent): Name the form: If p then q. Not q. Therefore not p.
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. The argument uses p → q.
  4. It denies q.
  5. Therefore ¬p follows by modus tollens.
  6. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: Modus tollens

3. Practice case C (Affirming the Consequent): Name the form: If p then q. If q then r. Therefore if p then r.

Choices: Hypothetical syllogism · Disjunctive syllogism · Denying the antecedent · Biconditional definition

Show solution
  1. Warm-up: First identify exactly what the question is asking: Practice case C (Affirming the Consequent): Name the form: If p then q. If q then r. Therefore if p then r.
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. The argument chains conditionals.
  4. p leads to q, and q leads to r.
  5. So p leads to r.
  6. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: Hypothetical syllogism

4. Practice case D (Affirming the Consequent): Name the form: p or q. Not p. Therefore q.

Choices: Disjunctive syllogism · Modus ponens · Affirming the consequent · Inverse

Show solution
  1. Warm-up: First identify exactly what the question is asking: Practice case D (Affirming the Consequent): Name the form: p or q. Not p. Therefore q.
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. The argument starts with an or statement.
  4. One option is ruled out.
  5. The remaining option follows.
  6. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: Disjunctive syllogism

5. Practice case E (Affirming the Consequent): Which form is invalid? If p then q. q. Therefore p.

Choices: Affirming the consequent · Modus ponens · Modus tollens · Disjunctive syllogism

Show solution
  1. Core Practice: First identify exactly what the question is asking: Practice case E (Affirming the Consequent): Which form is invalid? If p then q. q. Therefore p.
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. The conclusion may have another cause.
  4. q being true does not force p.
  5. So this is affirming the consequent.
  6. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: Affirming the consequent

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