4.6 Deduction and Induction

4.6 Deduction and Induction

(A) Reasoning by Deduction and Induction

1. Reasoning by deduction is a process of making a conclusion for a specific case based on a given general statement.

2. Reasoning by induction is a process of making a generalization based on specific cases.

Maths Tip
                       
1.     General statement  →  Special conclusion  → Deduction
2.     Specific cases  →  General conclusion  →  Induction


Example: 
Determine whether the following conclusion is made based on a deductive reasoning or inductive reasoning.
(a) Area of triangle = ½ × Base × Height
(i) 

Area of ∆ ABC
= ½ × 7cm × 5cm
= 17.5 cm2 





(ii)

Area of ∆ DEF
= ½ × 7cm × 4cm
= 14 cm2





(b)
1 = 7 (1)2 – 6
22 = 7 (2)2 – 6
57 = 7 (3)2 – 6
106 = 7 (4)2 – 6
 7n2 – 6, n = 1, 2, 3, 4…

Solution: 
(a)
The specific conclusion is made based on a general statement ~ Area of triangle = ½ × Base × Height. Therefore, the conclusion is made based on deductive reasoning.
(b) 
The general conclusion 7n2 – 6, n = 1, 2, 3, 4… is made based on specific cases. Therefore, the conclusion is based on inductive reasoning.