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
- Recognize why p → q, q, therefore p is invalid
- Explain the idea in plain English before using symbols
- Use examples, non-examples, or counterexamples to check the reasoning
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?
- Affirming the consequent uses p -> q and q.
- q might be true for another reason.
- Therefore p does not have to follow.
Answer: Invalid: something else could have made the field wet.
Lesson preview: this page shows 5 practice items. The interactive activity contains 20 practice items and 10 quiz items (multiple choice). Counts include repeated prompts and variants.
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
- Affirming the consequent uses p -> q and q.
- q might be true for another reason.
- Therefore p does not have to follow.
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
- Affirming the Consequent has the pattern p -> q; q; therefore p.
- Match the premises and conclusion to the pattern.
- 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
- Affirming the Consequent has a specific shape.
- p -> q; q; therefore p
- This form is a common invalid look-alike.
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
- Affirming the Consequent is a tempting but invalid form.
- Affirming the consequent uses p -> q and q.
- 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
- Invalid means the conclusion can fail while premises hold.
- q can be true for another reason, so p does not have to hold.
- 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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