A-Level Mathematics • Proof • A2

Proof by Deduction

Learn how to prove mathematical statements by starting with known facts and using valid logical deductions.

Video Lesson 12 Minutes Pure Mathematics Advanced Level

šŸŽ¬ Animated Lesson

šŸŽ™ Narration

Watch how a proof by deduction begins with established information and proceeds through a sequence of justified mathematical statements.

🧠 Key Idea

Proof by deduction uses accepted facts, definitions and algebraic reasoning to demonstrate that a conclusion must be true.

āœ… Learning Outcome

After completing this lesson you should be able to:

  • Identify assumptions in a proof
  • Construct a logical sequence of deductions
  • Justify each mathematical step
  • State a clear final conclusion

Worked Example

Prove that the sum of two consecutive integers is odd.

Let the first integer be n, where n is an integer.

The next consecutive integer is n + 1.

Their sum is n + (n + 1) = 2n + 1.

Since 2n is even, 2n + 1 is odd.

Therefore, the sum of two consecutive integers is always odd.

Quick Quiz

Which expression represents the sum of two consecutive integers, n and n + 1?

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