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
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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.