A-Level Mathematics · Proof · A2

Proof by deduction.

Use accepted facts and logical steps to establish a mathematical conclusion.

A2 Proof10 MinutesAnimated lesson

WATCH THE IDEA MOVE

Animated
explanation.

Pause, replay and follow every logical step at your own pace.

01 / KEY IDEA

Deduction starts from known facts and reaches a necessary conclusion through valid algebra and logic.

02 / LEARNING OUTCOMES
  • State an assumption clearly
  • Build a logical chain
  • Justify the final conclusion

WORKED EXAMPLE

Follow every
reason.

Prove that the sum of two odd integers is even.

01

Let the odd integers be 2a + 1 and 2b + 1.

02

Their sum is 2a + 1 + 2b + 1 = 2(a + b + 1).

03

Because a + b + 1 is an integer, the sum is even.

QUICK CHECK

Test the
logic.

Choose the statement that describes a valid mathematical proof.

What makes a mathematical proof valid?