Unit 2 Review and Checkpoint
A free Logic lesson from the “Statements and Negation” unit, with a worked example and practice problems including step-by-step solutions.
The exact negation holds in every case where the original fails and in no case where the original holds. Over real numbers, not greater than means less than or equal to. Not all means at least one not; not some means none. Check the boundary and avoid strengthening the claim. 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 simple statements, compound statements, and precise negation
- Choose the reasoning tool that matches the statement
- Explain why an answer is valid, invalid, true, false, or unsupported
Worked example
Problem. Negate x > 43 over the real numbers.
- The negation includes the boundary and all lower values.
Answer: x <= 43
Lesson preview: this page shows 5 practice items. The interactive activity contains 16 practice items and 16 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. Classify “Please list the first 7 primes.”
Choices: True statement · False statement · Universal theorem · Command; it has no truth value
Show solution
- An instruction requests an action rather than asserting a claim.
Answer: Command; it has no truth value
3. The sentence “The sealed envelope contains a blue card” refers to one particular envelope. How should it be classified before opening it?
Choices: Automatically false · A command · A statement whose truth is not yet known to us · Not a statement because it is unobserved
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
4. Over the integers, classify “x > 7” when no x is assigned or quantified.
Choices: A question · An open sentence (predicate) · A true statement · A false statement
Show solution
- Its truth depends on the value assigned to x.
- For example, x=8 satisfies it while x=6 does not.
Answer: An open sentence (predicate)
5. 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
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Practice Unit 2 Review and Checkpoint Take the free placement check