Truth Values: True, False, and Unknown
A free Logic lesson from the “Foundations of Logical Thinking” unit, with a worked example and practice problems including step-by-step solutions.
Evaluate a claim using the supplied information and domain. True, false and not yet known describe different situations; unknown is not a third truth value in the classical truth tables used here. For and, both parts must hold. Inclusive or needs at least one. If two permitted examples give different answers, the information is insufficient.
What you'll learn
- Distinguish true, false, and unknown claims
- Explain the idea in plain English before using symbols
- Use examples, non-examples, or counterexamples to check the reasoning
Worked example
Problem. Evaluate “57 is divisible by 2.”
- 57=2(28)+1 leaves remainder 1.
Answer: False
Lesson preview: this page shows 5 practice items. The interactive activity contains 6 practice items and 6 quiz items (multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Evaluate “27 is divisible by 2.”
Choices: False · True
Show solution
- 27=2(13)+1 leaves remainder 1.
Answer: False
2. Evaluate “15 > 13 and 15 < 14.”
Choices: True · False
Show solution
- The first part is true and the second is false.
- A conjunction needs both parts true.
Answer: False
3. Evaluate “13 > 14 or 26 is even.” Use inclusive or.
Choices: True · False
Show solution
- The first part is false and the second is true.
- Inclusive or needs at least one true part.
Answer: True
4. A hidden integer x satisfies x > 13. Can you decide whether x is even?
Choices: Yes, x must be even · Yes, x must be odd · There is no integer greater than the bound · Not from this information
Show solution
- 26 is an allowed even value; 27 is an allowed odd value.
- The premise does not determine parity.
Answer: Not from this information
5. Evaluate “Every integer in {13, 14, 15} is at least 13.”
Choices: True · False
Show solution
- Check each of the three listed domain values.
- Each is greater than or equal to the stated bound.
Answer: True
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