Menu

Math Lesson 9.3.6 - Rejecting a Supposition by Counter Example

Please provide a rating, it takes seconds and helps us to keep this resource free for all to use

[ 3 Votes ]

Welcome to our Math lesson on Rejecting a Supposition by Counter Example, this is the sixth lesson of our suite of math lessons covering the topic of Identities, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Rejecting a Supposition by Counter Example

Sometimes it is not worth trying to prove a supposition but it is enough to reject (disproof) it through a counter - example. Recall that a supposition must be always true to be accepted. If it is 1000 times true and only 1 time false, it is definitely regarded as false.

For example, if we claim that all odd numbers ending with 3 are prime, it is enough to find a counter - example (in this case, 33) to reject this claim. Let's consider an example to clarify this point better.

Example 5

Disprove by counter - example the claim that the sum of four consecutive numbers is always odd.

Solution 5

We take for example 7, 8, 9 and 10. Adding them yields

S = 7 + 8 + 9 + 10
= 34

Since this counter - example gave an even number as result, the original claim is false.

More Identities Lessons and Learning Resources

Equations Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
9.3Identities
Lesson IDMath Lesson TitleLessonVideo
Lesson
9.3.1Overview
9.3.2Identities, Conditional Identities (Equations) and Inconsistent Equations
9.3.3Identify Conditional Identities and Inconsistent Equations
9.3.4Eight Algebraic Identities
9.3.5Solving by Proof
9.3.6Rejecting a Supposition by Counter Example

Whats next?

Enjoy the "Rejecting a Supposition by Counter Example" math lesson? People who liked the "Identities lesson found the following resources useful:

  1. Reject Counter Example Feedback. Helps other - Leave a rating for this reject counter example (see below)
  2. Equations Math tutorial: Identities. Read the Identities math tutorial and build your math knowledge of Equations
  3. Equations Video tutorial: Identities. Watch or listen to the Identities video tutorial, a useful way to help you revise when travelling to and from school/college
  4. Equations Revision Notes: Identities. Print the notes so you can revise the key points covered in the math tutorial for Identities
  5. Equations Practice Questions: Identities. Test and improve your knowledge of Identities with example questins and answers
  6. Check your calculations for Equations questions with our excellent Equations calculators which contain full equations and calculations clearly displayed line by line. See the Equations Calculators by iCalculator™ below.
  7. Continuing learning equations - read our next math tutorial: Iterative Methods for Solving Equations

Help others Learning Math just like you

Please provide a rating, it takes seconds and helps us to keep this resource free for all to use

[ 3 Votes ]

We hope you found this Math tutorial "Identities" useful. If you did it would be great if you could spare the time to rate this math tutorial (simply click on the number of stars that match your assessment of this math learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of math and other disciplines.

Equations Calculators by iCalculator™