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Final Course Assessment

A free Logic lesson from the “Logic Applications and Final Review” unit, with a worked example and practice problems including step-by-step solutions.

The final Logic assessment is cumulative. It asks learners to translate claims, evaluate truth conditions, test arguments, use counterexamples, and explain reasoning clearly. Learning objective: Demonstrate readiness with statements, truth tables, arguments, quantifiers, counterexamples, 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

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 (Final Course Assessment): Worked example: Which rule or habit best matches Final Course Assessment?

  1. Final Course Assessment targets a specific reasoning habit.
  2. Final Course Assessment focuses on demonstrate readiness with statements, truth tables, arguments, quantifiers, counterexamples, and proof-ready explanations.
  3. The other choices either overclaim or change the logical relationship.

Answer: Final Course Assessment focuses on demonstrate readiness with statements, truth tables, arguments, quantifiers, counterexamples, and proof-ready explanations.

Practice problems

1. Practice case A (Final Course Assessment): Classify the sentence "The number 18 is divisible by 3."

Choices: Statement · Question · Command · Fragment

Show solution
  1. It makes a claim that can be checked.
  2. Logic starts by deciding whether a sentence makes a true-or-false claim.
  3. The best classification is Statement.

Answer: Statement

2. Practice case B (Final Course Assessment): Which is a compound statement?

Choices: x is positive and x is even. · x is positive. · What is x? · Solve for x.

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  1. Course Review: First identify exactly what the question is asking: Practice case B (Final Course Assessment): Which is a compound statement?
  2. Compare each choice with the stated logical rule, and eliminate choices that change the claim's meaning.
  3. A compound statement joins simpler claims.
  4. The word and connects two claims.
  5. So the first choice is compound.
  6. Verify the selected choice by checking that it preserves the stated logical meaning and that the other choices change the rule or claim.

Answer: x is positive and x is even.

3. Practice case C (Final Course Assessment): Simplify the double negation ¬¬p.

Show solution
  1. Course Review: First identify exactly what the question is asking: Practice case C (Final Course Assessment): Simplify the double negation ¬¬p.
  2. Read the statement in plain English first, then match the symbol, connective, quantifier, or argument form to that meaning.
  3. The first negation flips p.
  4. The second negation flips it back.
  5. So ¬¬p is equivalent to p.
  6. Check the response against the original logical form: it should match p without changing the meaning.

Answer: p

4. Practice case D (Final Course Assessment): Which symbolic form matches "p or q" in standard mathematical logic?

Choices: p ∨ q · p ∧ q · ¬p · p ↔ q

Show solution
  1. Course Review: First identify exactly what the question is asking: Practice case D (Final Course Assessment): Which symbolic form matches "p or q" in standard mathematical logic?
  2. Compare each choice with the stated logical rule, and eliminate choices that change the claim's meaning.
  3. The word or is represented by ∨.
  4. Standard mathematical or is inclusive.
  5. So p or q becomes p ∨ q.
  6. Verify the selected choice by checking that it preserves the stated logical meaning and that the other choices change the rule or claim.

Answer: p ∨ q

5. Practice case E (Final Course Assessment): In the row p=False, q=True, r=True, what is p ↔ q?

Choices: True · False

Show solution
  1. Course Review: First identify exactly what the question is asking: Practice case E (Final Course Assessment): In the row p=False, q=True, r=True, what is p ↔ q?
  2. For symbolic logic, translate the symbols into plain English, then apply the truth condition for the connective.
  3. p is False and q is True.
  4. A biconditional is true when both parts have the same truth value.
  5. The final value is False.
  6. Verify the selected choice by checking that it preserves the stated logical meaning and that the other choices change the rule or claim.

Answer: False

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