Unit 3 Review and Checkpoint
A free Logic lesson from the “And, Or, and Basic Connectives” unit, with a worked example and practice problems including step-by-step solutions.
Conjunction requires both parts; inclusive disjunction requires at least one. First evaluate each smaller claim, then combine them in the order set by parentheses. An English requirement using both must not be weakened to either. 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
- Review and, or, not, and mixed compound statements
- Choose the reasoning tool that matches the statement
- Explain why an answer is valid, invalid, true, false, or unsupported
Worked example
Problem. Complete the final column for p ∧ q. Row order (p,q): TT, TF, FT, FF.
- At T, T, p ∧ q is true.
- At T, F, p ∧ q is false.
- At F, T, p ∧ q is false.
- At F, F, p ∧ q is false.
Answer: T, F, F, F
Lesson preview: this page shows 4 practice items. The interactive activity contains 4 practice items and 4 quiz items (multiple choice). 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: T, F, F, F · F, T, T, T · F, F, F, F · T, F, F, T
Show solution
- At T, T, p ∧ q is true.
- At T, F, p ∧ q is false.
- At F, T, p ∧ q is false.
- At F, F, p ∧ q is false.
Answer: T, F, F, F
2. Complete the final column for p ∨ q. Row order (p,q): TT, TF, FT, FF.
Choices: F, F, F, T · F, T, T, F · T, T, T, T · T, T, T, F
Show solution
- At T, T, p ∨ q is true.
- At T, F, p ∨ q is true.
- At F, T, p ∨ q is true.
- At F, F, p ∨ q is false.
Answer: T, T, T, F
3. Entry to the laboratory requires a badge AND a reservation. Sam has a badge but no reservation. Does Sam qualify?
Choices: Only if the badge is blue · The rule says nothing about this case · No · Yes
Show solution
- Both requirements must be true.
- The missing reservation makes the conjunction false.
Answer: No
4. An alarm activates for smoke OR heat, using inclusive or. Both sensors activate. Does the alarm activate?
Choices: Cannot tell from the rule · Yes · No, exactly one sensor must activate · No, both cancel
Show solution
- Inclusive or permits either condition or both.
Answer: Yes
Practice this interactively with instant feedback and an AI tutor.
Practice Unit 3 Review and Checkpoint Take the free placement check