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Final Logic Readiness Review

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 review emphasizes transfer. Students practice explaining why a claim is true, false, equivalent, valid, invalid, or not yet supported. Learning objective: Prepare for the final assessment by explaining reasoning across topics. Prerequisite: No formal prerequisite. 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 Logic Readiness Review): Worked example: Which rule or habit best matches Final Logic Readiness Review?

  1. Final Logic Readiness Review targets a specific reasoning habit.
  2. Final Logic Readiness Review focuses on prepare for the final assessment by explaining reasoning across topics.
  3. The other choices either overclaim or change the logical relationship.

Answer: Final Logic Readiness Review focuses on prepare for the final assessment by explaining reasoning across topics.

Practice problems

1. Practice case A (Final Logic Readiness Review): 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 Logic Readiness Review): Which is a compound statement?

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

Show solution
  1. Warm-up: First identify exactly what the question is asking: Practice case B (Final Logic Readiness Review): 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 Logic Readiness Review): Simplify the double negation ¬¬p.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Practice case C (Final Logic Readiness Review): 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 Logic Readiness Review): Which symbolic form matches "p or q" in standard mathematical logic?

Choices: p ∨ q · p ∧ q · ¬p · p ↔ q

Show solution
  1. Warm-up: First identify exactly what the question is asking: Practice case D (Final Logic Readiness Review): 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 Logic Readiness Review): Lesson focus: Which transfer task would show readiness for Final Logic Readiness Review?

Choices: Apply prepare for the final assessment by explaining reasoning across topics in a new sentence or context. · Repeat the exact worked example without changing the context. · Pick an answer before identifying the claim parts. · Use a rule from another lesson because the words sound close.

Show solution
  1. A transfer task keeps the same objective but changes the surface context.
  2. Apply prepare for the final assessment by explaining reasoning across topics in a new sentence or context.
  3. That is a better mastery signal than memorizing a practice prompt.

Answer: Apply prepare for the final assessment by explaining reasoning across topics in a new sentence or context.

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