Math Problem Statement
Consider this statement.
If a number is divisible by 3, then it's odd.
Provide a counterexample that proves the statement is false. Explain your reasoning.
Type the correct answer in the box.
Solution
The statement "If a number is divisible by 3, then it's odd" is false. A counterexample that proves this statement is false is the number 6.
Reasoning:
- The number 6 is divisible by 3 (since 6 ÷ 3 = 2).
- However, 6 is not odd; it is an even number.
Thus, 6 is a counterexample that disproves the statement.
Do you want more details or have any questions?
Here are five related questions to consider:
- What is the definition of an odd number?
- How can we determine if a number is divisible by 3?
- Can you find another even number divisible by 3?
- What is the difference between an odd number and an even number?
- How would you rewrite the original statement to make it true?
Tip: When asked to disprove a statement, finding just one counterexample is enough.
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Math Problem Analysis
Mathematical Concepts
Number Theory
Divisibility
Formulas
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Theorems
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Suitable Grade Level
Grades 6-8
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