This Boolean Algebra Tutorial gives us a holistic view of what Boolean functions and calculations are and will surely aid in solving many mathematical problems related to Boolean algebra

Basic operations in Boolean algebra are as follows:

Conjunction: also denoted by an inverted V this operation basically is similar to the intersection operation. In this we have a specific formula. Actually this formula is derived by basic algebra intersection operation:

A intersection B = A + B – A V B - - - - - - -(1)

Here V is the union operation.

In Boolean Algebra we only deal with true or false here. So anything that is not true will be a false. We can also denote it by zero and one. Here one will denote a true and zero will denote a false.

Now let us state the complimentary operation. This is also called as the negation operation. It is a singular operand operation. That is in this we will need just one operand to calculate the result. Let us take an example. Say A = True. Now negation A will be false. This operation can be stated as :

Let A = True;

~ A

Output A. Now the value of A will be false.

Union operation has already been discussed. In Boolean we have certain Boolean Algebra Rules to be followed for the same. Let us take a quick look at them.

True union True = True

(True union False) or (false union true)= True

False union False = false

Similarly for intersection we have

True intersection true = true

True intersection false = false

False intersection false = false

As we can see both the operation are just opposite to each other. These are Boolean form of algebra rules. Let us state them in a more simplified way.

A + 1 = 1

A + 0 = A

A . 1 = A

A . 0 = 0

So it is all about the multiplication or the dot product and the addition with zeros and ones. A here can have any value that is one or zero. Boolean Algebra Examples can be:

Let a = 1

B = 0 so a . b = 1 . 0 = 0

Similarly let b = 0, ~ b = 1. This is an example of complimentary operation.

Other rules for the Boolean forms are:

~(~A ) = A

A + ~A = 1

A. ~A=0

~(A+B) = (~A) .(~B)

~(A.B) = (~A) + (~B)

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