Lecture 1: LOGIC: Boolean Algebra for class XII Computer Science Students

Date: 23.06.12

Introduction to Logic


The main ingredient in the study of logic is the principles and method used to distinguish between arguments that are valid and those that are not. Logic deals with reasoning and the ability to deduce or come to some reasonable conclusions. In everyday life we guess what is going to happen on the basis of past experiences; “It looks like its going to rain” we say meaning that it may rain today. If we wait around long enough then it may rain. This is an example of inductive reasoning
In mathematics we can discover whether or not a guess is correct by checking if our conclusions can be deduced from results already known. This is called deductive reasoning. (This portion of tutorial is taken from|yale.edu)

 Inductive Reasoning v/s Deductive Reasoning

Example of Inductive Reasoning:
All of the swans that all living beings have ever seen are white.
Therefore, all swans are white. 

This type of reasoning is based on general conceptions and tries to draw conclusions on the basis of previously laid down concepts and theories. In the above example, ALL LIVING BEINGS HAVE SEEN EVER SWANS AND FOUND THAT ALL SWANS ARE WHITE, THAT MEANS VARIOUS DIFFERENT EXAMPLES AND INSTANCES (STORIES, EVENTS) ARE BEING RECORDED IN HISTORY WHERE LIVING BEINGS HAVE SEEN WHITE SWANS. SO WE CONCLUDED OUR RESULT THAT ALL SWANS ARE WHITE.

Example of Deductive Reasoning:
All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.

This type of reasoning in contrast to inductive reasoning is not based on any general principle, rather it takes various examples and then mathematically tried to deduct accurate solutions. 'Mathematical induction' is a type of deductive reasoning, which can be easily seen in the above example, THE FIRST PREMISE STATES THAT ALL OBJECTS CLASSIFIED AS "MEN" HAVE THE ATTRIBUTE "MORTAL". THE SECOND PREMISE STATES THAT "SOCRATES" IS CLASSIFIED AS A "MAN" – A MEMBER OF THE SET "MEN". THE CONCLUSION THEN STATES THAT "SOCRATES" MUST BE "MORTAL" BECAUSE HE INHERITS THIS ATTRIBUTE FROM HIS CLASSIFICATION AS A "MAN".
(example and explanation taken from|wikipedia.org) 

Statements
The starting point of logic is a statement. A statement in the technical sense is declarative and is either true or false, but cannot be both simultaneously. In logic it is irrelevant whether a statement is true or false, the important thing is that it should be definitely one or the other. Logic statements must be either true or false.
A Statement: is a declarative sentence which is either true or false.
Examples of declarative statements:
(a) New Haven is a city in Connecticut.
(b) The month of June has thirty days.
(c) The moon is made of red cheese.
(d) Tomorrow is Saturday.
The following are not statements:
(a) Come to our party!
(b) Is your homework done?
(c) Close the door when you leave.
(d) Good by dear.
Those are not good statements because they cannot be considered true or false.
The basic type of sentence in logic is called a simple statement. A simple statement is one that has only one thought with no connecting word.
Examples of simple statements
(a) Three is a counting number.
(b) Ann is early for class
If we take a simple statement and join them with a connecting word such as and, or, if . . . then, not, if and only if, we form a new sentence called a complex or compound statement.
Compound Statements: are formed from the combination of two or more simple statements.
(a) Ann is early for class and she has her note books.

(b) Three is a counting number and is also a odd number.
(This portion of tutorial is taken from|yale.edu)

6 comments:

  1. Thanks for sharing about George Boole,The Boolean adjective. I am here to discuss a simple definition of Boolean logic as-Boolean logic is a system of symbolic logic which is used in computers.Study of mathematical operations performed on binary variables that can have only two values: true or false. It provides a set of rules called Boolean logic that are indispensable in digital computer-circuit and switching-circuit design.
    college algebra problems

    ReplyDelete
    Replies
    1. Thank you harun for appreciation, simple definition and link.

      Delete
  2. what is the diff. between a simple and declarative statement

    ReplyDelete
    Replies
    1. Declarative statement can either be true or false. (All statements are declarative)
      Like
      Trees give us wood to make furniture like doors. (This is true and you can take is that we telling something which can not be challenged)

      And statements which are having no connecting word (means they are not compound statements which means they are single lines and not a combination of two statements using connecting words like and, or, etc.)

      Delete
  3. i.e. simple statements can also be declarative statement...???

    ReplyDelete