Unit 8 Review and Checkpoint
A free Logic lesson from the “Argument Validity” unit, with a worked example and practice problems including step-by-step solutions.
Validity means there is no assignment with all premises true and the conclusion false. Build such a countermodel to show invalidity. Modus ponens and modus tollens preserve truth; affirming the consequent does not. A valid form can still have false premises, so validity alone is not soundness. This review checks performance on mathematical tasks. For extended written work, use the separate rubric with a tutor or teacher; the automatic quiz does not certify proof-writing proficiency.
What you'll learn
- Review valid forms, invalid forms, and argument testing
- Choose the reasoning tool that matches the statement
- Explain why an answer is valid, invalid, true, false, or unsupported
Worked example
Problem. Premises: p→q and p. Is the conclusion q forced?
- The first premise guarantees q whenever p holds.
- The second premise supplies p.
Answer: Yes, by modus ponens
Lesson preview: this page shows 4 practice items. The interactive activity contains 4 practice items and 4 quiz items (multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Premises: p→q and p. Is the conclusion q forced?
Choices: No; it affirms the consequent · No; it denies the antecedent · Yes, because q is always true · Yes, by modus ponens
Show solution
- The first premise guarantees q whenever p holds.
- The second premise supplies p.
Answer: Yes, by modus ponens
2. Premises: p→q and q. Which assignment refutes the conclusion p?
Choices: p=false, q=false · There is no counterexample · p=false, q=true · p=true, q=false
Show solution
- Both premises are true in the selected row, yet p is false.
Answer: p=false, q=true
3. Premises: p→q and ¬q. What follows?
Choices: p ∧ q · ¬p · p · q
Show solution
- A true p would require q.
- Since q is false, p cannot be true.
Answer: ¬p
4. Premises: p∨q and ¬p. What follows?
Choices: q · ¬q · p · p ∧ q
Show solution
- The disjunction needs at least one true part.
- p is excluded, so q must hold.
Answer: q
Practice this interactively with instant feedback and an AI tutor.
Practice Unit 8 Review and Checkpoint Take the free placement check