Unit 4 Review and Checkpoint
A free Logic lesson from the “Truth Tables” unit, with a worked example and practice problems including step-by-step solutions.
This checkpoint checks row-by-row reasoning and the habit of reading table results back into words. Learning objective: Review truth tables for not, and, or, and compound statements. 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
- Review truth tables for not, and, or, and compound statements
- Choose the reasoning tool that matches the statement
- Explain why an answer is valid, invalid, true, false, or unsupported
Worked example
Problem. Example case A (Unit 4 Review and Checkpoint): A truth table with three variables has how many rows?
- Checkpoint Practice: First identify exactly what the question is asking: Example case A (Unit 4 Review and Checkpoint): A truth table with three variables has how many rows?
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Each variable has two truth values.
- Three variables create 2 x 2 x 2 cases.
Answer: 8
Practice problems
1. Practice case A (Unit 4 Review and Checkpoint): A truth table with three variables has how many rows?
Show solution
- Checkpoint Practice: First identify exactly what the question is asking: Practice case A (Unit 4 Review and Checkpoint): A truth table with three variables has how many rows?
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Each variable has two truth values.
- Three variables create 2 x 2 x 2 cases.
- That gives 8 rows.
- Check the result by substituting or estimating: the response should match 8 and make sense in the original problem.
Answer: 8
2. Practice case B (Unit 4 Review and Checkpoint): If p is True and q is True, what is p ∨ q?
Choices: True · False
Show solution
- Checkpoint Practice: First identify exactly what the question is asking: Practice case B (Unit 4 Review and Checkpoint): If p is True and q is True, what is p ∨ q?
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- The connective ∨ means inclusive or.
- It is true when at least one part is true.
- Here p ∨ q is True.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: True
3. Practice case C (Unit 4 Review and Checkpoint): Simplify the double negation ¬¬p.
Show solution
- Checkpoint Practice: First identify exactly what the question is asking: Practice case C (Unit 4 Review and Checkpoint): Simplify the double negation ¬¬p.
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- The first negation flips p.
- The second negation flips it back.
- So ¬¬p is equivalent to p.
- Check the result by substituting or estimating: the response should match p and make sense in the original problem.
Answer: p
4. Practice case D (Unit 4 Review and Checkpoint): In the row p=True, q=False, r=False, what is p → q?
Choices: True · False
Show solution
- Checkpoint Practice: First identify exactly what the question is asking: Practice case D (Unit 4 Review and Checkpoint): In the row p=True, q=False, r=False, what is p → q?
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- p is True and q is False.
- A conditional is false only when p is true and q is false.
- The final value is False.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: False
5. Practice case E (Unit 4 Review and Checkpoint): A club requires "age 12 or older and permission slip signed." Which connective joins the two requirements?
Choices: and · or · if and only if · not
Show solution
- Checkpoint Practice: First identify exactly what the question is asking: Practice case E (Unit 4 Review and Checkpoint): A club requires "age 12 or older and permission slip signed." Which connective joins the two requirements?
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- Both requirements must be met.
- When two conditions are both required, use and.
- So the connective is and.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: and
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