Unit 1 Review and Checkpoint
A free Logic lesson from the “Foundations of Logical Thinking” unit, with a worked example and practice problems including step-by-step solutions.
This checkpoint mixes the first unit's reasoning habits so learners can separate claims, reasons, conclusions, truth, and validity before symbols become heavier. Learning objective: Review statements, truth values, arguments, validity, and proof-ready explanations. 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 statements, truth values, arguments, validity, and proof-ready explanations
- 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 1 Review and Checkpoint): Classify the sentence "The number 18 is divisible by 3."
- It makes a claim that can be checked.
- Logic starts by deciding whether a sentence makes a true-or-false claim.
- The best classification is Statement.
Answer: Statement
Practice problems
1. Practice case A (Unit 1 Review and Checkpoint): Classify the sentence "The number 18 is divisible by 3."
Choices: Statement · Question · Command · Fragment
Show solution
- It makes a claim that can be checked.
- Logic starts by deciding whether a sentence makes a true-or-false claim.
- The best classification is Statement.
Answer: Statement
2. Practice case B (Unit 1 Review and Checkpoint): Which is a compound statement?
Choices: x is positive and x is even. · x is positive. · What is x? · Solve for x.
Show solution
- Checkpoint Practice: First identify exactly what the question is asking: Practice case B (Unit 1 Review and Checkpoint): Which is a compound statement?
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- A compound statement joins simpler claims.
- The word and connects two claims.
- So the first choice is compound.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: x is positive and x is even.
3. Practice case C (Unit 1 Review and Checkpoint): 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
- Checkpoint Practice: First identify exactly what the question is asking: Practice case C (Unit 1 Review and Checkpoint): Name the form: If p then q. If q then r. Therefore if p then r.
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- The argument chains conditionals.
- p leads to q, and q leads to r.
- So p leads to r.
- 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 (Unit 1 Review and Checkpoint): Reasoning by cases is appropriate when:
Choices: the cases cover all possibilities · only one example is checked · the conclusion is ignored · the domain is unknown
Show solution
- Casework splits a problem into possibilities.
- The proof is complete only if every possibility is covered.
- Then each case can be handled separately.
Answer: the cases cover all possibilities
5. Practice case E (Unit 1 Review and Checkpoint): Which sentence is a premise in "If a figure is a square, then it has four sides. This figure is a square. So it has four sides."?
Choices: This figure is a square. · So it has four sides. · Four is even. · The answer is 4.
Show solution
- A premise is a reason used to support the conclusion.
- This figure is a square is one of the reasons.
- The conclusion is that it has four sides.
Answer: This figure is a square.
Practice this interactively with instant feedback and an AI tutor.
Practice Unit 1 Review and Checkpoint Take the free placement check