Contradiction Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Contradiction.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
A mathematical statement that is always false — no values of the variables can ever make it true.
x + y = 5 AND x + y = 7 can't both be true simultaneously — this is a contradiction.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Contradictions signal an inconsistent system with no solutions.
Common stuck point: When you reach 0 = 3 or any false number statement, stop immediately — the system has no solution.
Sense of Study hint: Write out the simplified result. If it says something like 0 = 3, that means the system has no solution.
Worked Examples
Example 1
easySolution
- 1 Step 1: Subtract x from both sides: 1 = 3.
- 2 Step 2: 1 \neq 3. This is always false.
- 3 Step 3: No value of x can make this true — it's a contradiction.
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
mediumRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.