Deductive Reasoning in Mathematics

 Definition:

It is defined as a reasoning that builds or estimates deductive debates. In a lay man's understanding it is reasoning from the cause to the effect. The debate is valid iff the inference does follow necessarily from the assumption. Logic is made use from assumptions to inferences. If the debate is not valid then it is invalid i.e., it has one or more false assumptions.

An example of a deductive debate and therefore, deductive reasoning:

• All women are mothers
• Mother Teresa is a woman
• (Hence) Mother Teresa is a mother

Inductive Reasoning:

Inductive reasoning moves from the effect to the cause.

For example,

The milkman came in the morning.

The milkman came yesterday.

The milkman came day before yesterday.

'

'

Hence, the milkman comes every day and will turn up the following day also.

One has to note that while a inference got by deduction must be true if the

assumptions are true, the inference induced by induction may or may not be true.

For example,

Patients who stay in the hospital for short periods often find that surgeries are conducted every day of their stay. They could infer that surgeries are done every day in the hospital - but it could not be true.

Inductive Vs Deductive:

Deductive reasoning works from general to specific, while inductive reasoning works from specific to general. Informally, we otherwise call deductive reasoning as 'top bottom' approach, whereas, inductive reasoning 'bottom up' approach. Thus, in mathematics, inductive reasoning is made use often to make a guess at a property and then deductive reasoning is made use of to prove that the property must hold good for all or some delimited set of cases.

Summary:

Psychologists do experiments and construct models and theories to realize how people make deductive conclusions.