__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 Tip1. General
statement → Special conclusion → Deduction2. 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 cm

^{2}

**(ii)**

Area
of ∆

*DEF*
=
½ × 7cm × 4cm

=
14 cm

^{2}

**(b)**

1
= 7 (1)

^{2}– 6
22
= 7 (2)

^{2}– 6
57
= 7 (3)

^{2}– 6
106
= 7 (4)

^{2}– 6
7

*n*^{2}– 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**7*n*^{2}– 6,*n*= 1, 2, 3, 4… is made based on**specific cases**. Therefore, the conclusion is based on**inductive reasoning**.