A concise Approach on Understanding Boolean Algebra

Boolean algebra is branch of mathematics that has specific set of rules and theorems which helps us express and manipulate logical expression mathematically. That’s typical text book introduction you will find. But why would you be searching around the web if you settled for that definition? Probably you are searching for more examples or you are one of those self learners.

You are already using Boolean logic in your life . for example consider this statement, “if are going to grocery store get me a ice-cream or soda “. You know it already what that statement is trying to clarify but just to make it professional it means you want anything between ice-cream and soda and The word “OR” is a connective that binds the set {ice-cream,soda}. What if you wanted to use “AND” connective instead of “OR”. you would have wanted both ice-cream and soda which would lead to different situation.  If the statement above was said by you to your friend then lets take a look at all the possibilities about your friend bringing goods you want and have a deeper look at how connectives can change the situation.Item was bought then it will be marked TRUE else marked FALSE.

AND connective :”Bring me ice-cream and soda”
OR connective: “Bring me ice-cream or soda”

Ice-creamsodaAND connectiveOR connective
TRUEFALSEFALSETRUE
FALSEFALSEFALSEFALSE
TRUETRUETRUETRUE
FALSETRUEFALSETRUE

In the first situation , your friend bought ice-cream but not soda so your statement with AND connective is false but the statement with OR connective is true. i leave the interpretation of each row to yourself because you are already familiar with such stuffs.

Getting steps into Boolean Algebra

Expressing mathematically means there is conversion of statements into operation. and Typically every operation has operand and operator. When you are enjoying a ride on passenger bus from New York to Alabama, don’t forget that driver is operator and passengers are operand and your operation is to reach to Alabama from New York.

With respect to textbook standards, Operator is a symbol that causes specific mathematical operation or logical operation to be performed. Operand are part of operation on which operator perform their tasks

 

Note : Boolean algebra  can have only two possible outputs “TRUE or FALSE” .there are other ways of saying true and false too such as “YES/NO” ,”1/0″,”HIGH/LOW” etc

Types of operators in Boolean Algebra

Boolean OperatorsMathematical symbolExpression
AND.A.B
OR +A+B
NOT~~A

AND Operator

Operator that yields positive output or True as output if all the operand involved in operation are  True then it is AND operator.

ABA AND B(A.B)
TRUEFALSEFALSE
FALSEFALSE FALSE
TRUETRUE TRUE
FALSE TRUE FALSE

 

OR Operator

Operator that yields positive output or True as output if any of the operand involved in operation are  True then it is AND operator.

ABA OR B(A+B)
TRUEFALSETRUE
FALSEFALSEFALSE
TRUETRUETRUE
FALSETRUE FALSE

NOT Operator

Operator that yields opposite of operand is NOT operator. If x is true then NOT X(~X) is false and vice versa.

A~A
TRUEFALSE
FALSE TRUE

 

 

 

 

This is Ashish Thapa. It's just a name after all. Just had a thought that our names should signify our situation and should be dynamic. What if our name upgraded with respect to experiences acquired.

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