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.
Translate a practical rule into precise conditions, evaluate the conditions, and limit the conclusion to what they support. Algebraic transformations may need candidate checks; geometric pictures need marked or given facts; observational associations do not alone establish causation. Universal instructions require every specified case. 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
- Prepare for the final assessment by explaining reasoning across topics
- Explain the idea in plain English before using symbols
- Use examples, non-examples, or counterexamples to check the reasoning
Worked example
Problem. A program permits access when registered AND (member OR guest). For registered=true, member=false, guest=true, what happens?
- member OR guest is true.
- registered AND true is true.
Answer: Access is permitted
Lesson preview: this page shows 5 practice items. The interactive activity contains 30 practice items and 30 quiz items (multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Which sentence makes a claim with a truth value?
Choices: 15 is an even integer. · Calculate 15 + 2. · Is 15 even? · What an interesting number!
Show solution
- A false declarative claim is still a statement.
- 15 is odd, so the selected statement is false rather than not a statement.
Answer: 15 is an even integer.
2. The sentence “The sealed envelope contains a blue card” refers to one particular envelope. How should it be classified before opening it?
Choices: Not a statement because it is unobserved · Automatically false · A command · A statement whose truth is not yet known to us
Show solution
- Whether we know the truth is different from whether the sentence makes a definite claim.
Answer: A statement whose truth is not yet known to us
3. Evaluate “9 > 7 and 9 < 8.”
Choices: False · True
Show solution
- The first part is true and the second is false.
- A conjunction needs both parts true.
Answer: False
4. Rewrite “x is at most 7” exactly.
Choices: x = 7 · x <= 7 · x < 7 · x >= 7
Show solution
- At most includes the boundary and every smaller value.
Answer: x <= 7
5. All members are registered. Ada is a member. Which premise is needed to conclude Ada is registered?
Choices: All members are registered · All registered people are members · No members are registered · Ada is registered
Show solution
- The universal premise connects membership to registration.
- Do not assume the desired conclusion as the missing reason.
Answer: All members are registered
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