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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.

List every truth assignment systematically. For two variables use TT, TF, FT, FF. Add an intermediate column for each subexpression, then compute the outer connective. Implication is false only at true antecedent and false consequent; a biconditional is true when the values agree. This review checks performance on mathematical tasks. For extended written work, use the separate rubric with a tutor or teacher; the automatic quiz does not certify proof-writing proficiency.

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. Complete the final column for ¬p ∨ q. Row order (p,q): TT, TF, FT, FF.

  1. At T, T, ¬p ∨ q is true.
  2. At T, F, ¬p ∨ q is false.
  3. At F, T, ¬p ∨ q is true.
  4. At F, F, ¬p ∨ q is true.

Answer: T, F, T, T

Lesson preview: this page shows 5 practice items. The interactive activity contains 8 practice items and 8 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.

Practice problems

1. Complete the final column for ¬p ∨ q. Row order (p,q): TT, TF, FT, FF.

Choices: F, T, F, F · F, F, T, T · T, F, T, F · T, F, T, T

Show solution
  1. At T, T, ¬p ∨ q is true.
  2. At T, F, ¬p ∨ q is false.
  3. At F, T, ¬p ∨ q is true.
  4. At F, F, ¬p ∨ q is true.

Answer: T, F, T, T

2. Complete the final column for p ∧ ¬q. Row order (p,q): TT, TF, FT, FF.

Choices: T, T, F, F · F, T, F, T · F, T, F, F · T, F, T, T

Show solution
  1. At T, T, p ∧ ¬q is false.
  2. At T, F, p ∧ ¬q is true.
  3. At F, T, p ∧ ¬q is false.
  4. At F, F, p ∧ ¬q is false.

Answer: F, T, F, F

3. Complete the final column for p ↔ q. Row order (p,q): TT, TF, FT, FF.

Choices: T, F, F, F · T, F, F, T · F, T, T, F · F, F, F, T

Show solution
  1. At T, T, p ↔ q is true.
  2. At T, F, p ↔ q is false.
  3. At F, T, p ↔ q is false.
  4. At F, F, p ↔ q is true.

Answer: T, F, F, T

4. Complete the final column for ¬(p ∨ q). Row order (p,q): TT, TF, FT, FF.

Choices: F, F, F, T · T, T, T, F · T, F, F, T · F, F, F, F

Show solution
  1. At T, T, ¬(p ∨ q) is false.
  2. At T, F, ¬(p ∨ q) is false.
  3. At F, T, ¬(p ∨ q) is false.
  4. At F, F, ¬(p ∨ q) is true.

Answer: F, F, F, T

5. Complete the final column for (p ∧ q) ∨ r. Row order (p,q,r): TTT, TTF, TFT, TFF, FTT, FTF, FFT, FFF.

Choices: F, F, F, T, F, T, F, T · F, T, T, F, T, F, T, F · T, T, T, F, T, F, T, T · T, T, T, F, T, F, T, F

Show solution
  1. At T, T, T, (p ∧ q) ∨ r is true.
  2. At T, T, F, (p ∧ q) ∨ r is true.
  3. At T, F, T, (p ∧ q) ∨ r is true.
  4. At T, F, F, (p ∧ q) ∨ r is false.
  5. At F, T, T, (p ∧ q) ∨ r is true.
  6. At F, T, F, (p ∧ q) ∨ r is false.
  7. At F, F, T, (p ∧ q) ∨ r is true.
  8. At F, F, F, (p ∧ q) ∨ r is false.

Answer: T, T, T, F, T, F, T, F

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