__4.6 Deduction and Induction__

(A) Reasoning by 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**.

**Reasoning by**

2.

2.

**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}– 622 = 7 (2)

^{2}– 657 = 7 (3)

^{2}– 6106 = 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)

(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**.