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# Inductive and Deductive Logic

July 15, 2022
written by Azhar Ejaz

In daily life, we often draw general conclusions from a limited number of observations or experiences. These are inductive and deductive logic. A person gets a penicillin injection once or twice and experiences a reaction soon often words. He generalizes that he is allergic to penicillin.

## What is induction?

The method of drawing conclusions on the basis of a limited number of observations or experiences is called induction.

For example:

A person gets a penicillin injection once or twice and experiences a reaction soon afterward. He generalizes he is allergic to penicillin.

## What is the deduction?

To draw conclusions from accepted or well-known facts is called deduction.

For example:

All men are mortal. We are men so we are mortal.

## What is the postulate?

Some statements which are accepted as true without proof are called postulates.

## What is a proposition?

A declarative statement that may be true or false but not both is called a proposition.

## What is Aristotelian logic?

Deductive logic in which every statement is regarded as true or false and there is no other possibility is called the Aristotelian logic.

## What is Non-Aristotelian logic?

Deductive logic in which there is scope for a third or fourth possibility is called Non-Aristotelian logic.

## What is Negation logic?

If p is any proposition, its negation is denoted by ~p. Thus if a statement p is true, ~p is false and if a statement p is false ~p is true.

The truth table is given as:

## What is the conjunction of two statements?

The conjunction of two statements P and q is denoted by p^q and it is true and only if both of its components are true .in all other cases, it is false.

The truth table of p^q is given as:

## What is the disjunction?

Disjunction of two statements p and q is denoted by pvq and is true if at least one of the statements is true.

It is false when both of them are false.

The truth table of pvq is:

## What is conditional /implication?

A compound statement of the form if p then q .written as pâ€¦â€¦> q.is called a conditional or an implication .P is called the antecedent or hypothesis and q is called the consequent or conclusion.

A conditional is regarded as false only when the antecedent is true and the consequent is false .in all other cases. It is considered to be true.

The truth table is

## What is biconditional?

The proposition pâ€¦â€¦â€¦>q^qâ€¦â€¦..>p is written as p<â€¦â€¦â€¦>q and is called the biconditional or equivalence.

The bio conditional is considered true when both p and q are true or both p and q are false.

The truth table of p iff q is:

## What is the converse of pâ€¦â€¦.>q?

let pâ€¦â€¦.>q be a given conditional .than qâ€¦â€¦..>p is called the converse of pâ€¦â€¦>q .

its truth table is:

## What is the inverse of the conditional pâ€¦â€¦â€¦>q?

Let pâ€¦â€¦.>q be is a given conditional,~pâ€¦â€¦>~q is called the inverse of pâ€¦..>q,

Its truth table is:

## What is the contrapositive of pâ€¦..>q?

let pâ€¦..>q be a given conditional,~qâ€¦..>~p is called the  contrapositive  of pâ€¦â€¦>q,

it truth table is:

## What is a tautology?

A statement that is true for all the possible values of the variable involved in it is called tautology.

## What is the absurdity?

A statement that is always false is called an absurdity or a contradiction.

For example:

pâ€¦â€¦>~q is an absurdity.

## What is a contingency?

A statement that can be true or false depending upon the truth values of the variables involved in it is called a contingency.

## What is the quantifier?

The words or symbols which convey the idea of quantity or number are called quantifiers.

### Types of the quantifiers:

There are two types of quantifier

1. Universal quantifiers.
2. Existential quantifier.

### What are universal quantifiers?

The symbol  âˆ€   used, for all is a universal quantifier.

### What is an Existential quantifier?

The symbol! âˆƒ is used for there exist is an existential quantifier.

## Prove that in any universe the empty set {} is a subset of any set A.

Proof:

Let U be a universal set.

Considered the conditional that âˆ€  xâˆˆU,xâˆˆÏ†â€¦â€¦>xâˆˆA

The antecedent or hypothesis of this conditional is false because no xâˆˆU is a member of Ï†.

Hence the conditional is true because a conditional is false only when the antecedent is true and the conclusion is false.

## Frequently Asked Question-FAQs

### What is induction?

The method of drawing conclusions on the basis of a limited number of observations or experiences is called induction.

### What is the deduction?

To draw conclusions from accepted or well-known facts is called deduction.

### What is a contingency?

A statement that can be true or false depending upon the truth values of the variables involved in it is called a contingency.

### Types of the quantifiers:

There are two types of quantifier
Universal quantifiers.
Existential quantifier.

### What is the quantifier?

The words or symbols which convey the idea of quantity or number are called quantifiers.

### What is a tautology?

A statement that is true for all the possible values of the variable involved in it is called tautology.

### What is the absurdity?

A statement that is always false is called an absurdity or a contradiction.

### What is Aristotelian logic?

Deductive logic, which is the kind of logic that regards every statement as either true or false and nothing else, is called Aristotelian logic.

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