Double Math

# Inductive and Deductive Logic

## Induction:-

In daily life we draw conclusions from a limited number of observations. A person gets penicillin injection once or twice and experiences reaction soon afterwards. He generalises that he is allergic to penicillin. We generally form opinions about others on the basis of a few contacts only. This way of drawing conclusions is called induction.
Inductive reasoning is useful in natural sciences where we have to depend upon repeated experiments or observations. In fact greater part of our knowledge is based on induction.

## Deduction:-

On many occasions we have to adopt the opposite course. We have to draw conclusions from accepted or well-known facts. We often consult lawyers or doctors on the basis of their good reputation. This way of reasoning i.e., drawing conclusions from premises believed to be true, is called deduction. One usual example of deduction is: All men are mortal. We are men. Therefore, we are also mortal. Deduction is much used in higher mathematics. In teaching elementary mathematics we generally resort to the inductive method. For instance the following sequences can be continued, inductively, to as many terms as we like:

i) 2,4,6,…

(ii) 1,4,9,…

iii) 1,-1,2,-2,3,-3,…

iv) 1,4,7,…

iv) 1,4,7,…

To start with we accept a few statements (called postulates) as true without proof and draw as many conclusions from them as possible. Basic principles of deductive logic were laid down by Greek philosopher, Aristotle.The illustrious mathematician Euclid used the deductive method while writing his 13 books of geometry, called Elements. Toward the end of the 17th century the eminent German mathematician, Leibniz, symbolized deduction. Due to this device deductive method became far more useful and easier to apply.