math f4 chapter 4 mathematical reasoning

1. 4.6 Deduction and
induction

2. Deduction
A process of making a specific
conclusion from a general
statement.

3. Example 1 : deduction
The area of a circle with radius is πr ².
A circle has a radius of 7 cm.

4. Example 2 : deduction
All factors of 8 are factors of 24. 4
is a factor of 8.

5. Example 3 : deduction
Given the sum of the interior angles of
an n-sides polygon is (n – 2) x 180⁰.
Polygon x has 8 sides.

6. Example 4 : deduction
A set with n elements has 2ⁿ subsets.
Set P has 5 elements .

7. Example 5 : deduction

8. Example 6 : deduction

9. Example 7 : deduction

10. Example 8 : deduction

11. Example 9 : deduction

12. Example 10 : deduction

13. Induction
A process of making a
general conclusion form
specific cases.

14. Example 1 : induction

15. Example 2 : induction

16. Example 3 : induction

17. Example 4 : induction

18. Example 5 : induction

19. Example 6 : induction

20. Example 7 : induction

21. Answer example 7

22. Example 8 : induction

23. Example 9 : induction

24. Example 10 : induction

25. Example 11 : induction
Make a general conclusion by induction for the
sequence of numbers 8, 17, 32, 53, …, which
follows the pattern below.
8 = 5 + 3(1)²
17 = 5 + 3(2)²
32 = 5 + 3(3)²
53 = 5 + 3(4)²
…