Practice Contradiction in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick 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.

Showing a random 20 of 50 problems.

Example 1

easy
Is 0=0 a contradiction or an identity?

Example 2

medium
Elimination on a 3×3 system yields 0=1 in one row. What can you conclude?

Example 3

medium
Solve 2x−1=2x−1+5.

Example 4

easy
Does reaching 0=3 mean you made an arithmetic error?

Example 5

easy
Is 0=5 ever true?

Example 6

easy
True or false: x=−2 has no real solution.

Example 7

easy
Does x2=−9 have a real solution?

Example 8

hard
Prove by contradiction that there is no smallest positive real number.

Example 9

medium
Does {2x=6, 2x=10} contain a contradiction?

Example 10

medium
Does the system {x+y>5, x+y<2} have a solution?

Example 11

medium
Solve ∣x−3∣=−1.

Example 12

easy
How many solutions does 3(x+2)=3x+6 have?

Example 13

medium
What is the difference between a contradiction and an identity in elementary algebra?

Example 14

medium
After elimination you get 0=0. Is this a contradiction?

Example 15

medium
Solve 2(x+3)=2x+5.

Example 16

easy
System reduces to 0=−2. How many solutions?

Example 17

medium
Solve 5(x−2)−3x=2x+7.

Example 18

medium
If a derivation under your assumption produces a contradiction, what can you conclude about the assumption?

Example 19

medium
Does the system {y=2x+1, y=2x−3} have a solution?

Example 20

easy
Can x+3=x+7 have a solution?
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Related Concepts

EquationsConsistency