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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.

This checkpoint checks whether learners can tell good reasoning from tempting look-alikes. Learning objective: Review valid forms, invalid forms, and argument testing. Prerequisite: Review the lessons in this unit before starting.. Work in this lesson starts with ordinary language, then connects the idea to symbols only after the meaning is clear. Example 1: A truth-table question asks for cases; a counterexample question asks for one case that breaks a claim. Example 2: A validity question asks whether the conclusion must follow, not whether the sentences sound realistic. 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: Mixed review builds the habit of choosing the right reasoning tool for the claim in front of you.

Worked example

Problem. Example case A (Unit 8 Review and Checkpoint): Name the form: If p then q. p. Therefore q.

  1. Checkpoint Practice: First identify exactly what the question is asking: Example case A (Unit 8 Review and Checkpoint): 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 (Unit 8 Review and Checkpoint): Name the form: If p then q. p. Therefore q.

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

Show solution
  1. Checkpoint Practice: First identify exactly what the question is asking: Practice case A (Unit 8 Review and Checkpoint): 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 (Unit 8 Review and Checkpoint): In "If a figure is a square, then the figure is a rectangle," what is the conclusion?

Choices: the figure is a rectangle · a figure is a square · if · only if

Show solution
  1. The conclusion is the then-part.
  2. It is what follows if the hypothesis holds.
  3. Here the conclusion is the figure is a rectangle.

Answer: the figure is a rectangle

3. Practice case C (Unit 8 Review and Checkpoint): In the row p=True, q=False, r=True, what is p ∨ q?

Choices: True · False

Show solution
  1. Checkpoint Practice: First identify exactly what the question is asking: Practice case C (Unit 8 Review and Checkpoint): In the row p=True, q=False, r=True, what is p ∨ q?
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. p is True and q is False.
  4. An inclusive-or statement is true when at least one part is true.
  5. The final value is True.
  6. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: True

4. Practice case D (Unit 8 Review and Checkpoint): Name the form: p or q. Not p. Therefore q.

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

Show solution
  1. Checkpoint Practice: First identify exactly what the question is asking: Practice case D (Unit 8 Review and Checkpoint): 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 (Unit 8 Review and Checkpoint): If p is False and q is True, what is p → q?

Choices: True · False

Show solution
  1. Checkpoint Practice: First identify exactly what the question is asking: Practice case E (Unit 8 Review and Checkpoint): If p is False and q is True, what is p → q?
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. A conditional is false only when p is true and q is false.
  4. Here p is False and q is True.
  5. So p → q is True.
  6. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: True

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