SUMMARY
The statement "If a|b and a|c, then one (or both) of b|c or c|b holds" is false. A counter-example is provided with a = 5, b = 10, and c = 15, demonstrating that neither 10 divides 15 nor 15 divides 10. This disproves the original claim effectively by showing that the divisibility relationship does not necessarily hold in all cases.
PREREQUISITES
- Understanding of divisibility notation (a|b)
- Basic knowledge of discrete mathematics
- Familiarity with constructing mathematical proofs
- Ability to create counter-examples in mathematical arguments
NEXT STEPS
- Study the properties of divisibility in number theory
- Learn about constructing and analyzing mathematical proofs
- Explore counter-examples in mathematical logic
- Investigate related concepts such as greatest common divisors and least common multiples
USEFUL FOR
Students of discrete mathematics, educators teaching number theory, and anyone interested in mathematical proofs and logic.