A function in the form of f: Pk ⇢ P, where the values of P = 0, 1 and value of ‘k’ is non- negative Integer is known as Boolean function. Now we will see what is Boolean Algebra? Both boolean algebra and Boolean logic are same terms. It is used to find the algebra of real Numbers but it is used for some numeric operations which is multiplication pq, addition p + q and negative values are replaced by some logical operations of conjunction and disjunction and negations. These are the operations of Boolean algebra.
Boolean algebra has different structures which are represented by 'Hasse diagram'.
If a Boolean function has two binary operations i.e. logical AND or we can say “widge” and the notation of AND operation is “∧” and other operation is logical OR or we can say “vee”, the notation of ‘OR’ logical operation is “∨” and both operations satisfy different type of laws which are shown below:
Suppose P ∧ P = P ∨ P = P,
These logical operations also satisfy the commutative laws:
Let P ∧ Q = Q ∧ P;
And P ∨ Q = Q ∨ P;
Now we will see how it satisfies the associative laws:
⇒ P ∧ (Q ∧ R) = (P ∧ Q) ∧ R;
⇒ P ∨ (Q ∨ R) = (P ∨ Q) ∨ R;
The operation satisfies the absorption laws:
⇒ P ∧ (P ∨ Q) = P ∨ (P ∧ Q) = P;
The operations are manually distributive:
⇒ P ∧ (Q ∨ R) = (P ∧ Q) ∨ (P ∧ R);
⇒ P ∨ (Q ∧ R) = (P ∨ Q) ∧ (P ∨ R);
‘P’ contains universal bounds ∅ (empty Set) and I (the universal set) which satisfy:
⇒ ∅ ∧ P = ∅;
⇒ ∅ ∨ P = P;
⇒ I ∧ P = P;
⇒ I ∨ P = I;
This is all about Boolean algebra.
Boolean Algebra can be considered as logical Calculus which is widely used in digital computer system. Possibility of happening something may be either true of false. Boolean algebra is also based on true and false. True and false are pointed by ‘1’ and ‘‘0’ respectively in boolean algebra.
If there are two variables A and B then there are four possible combi...Read More
A function in the form f: Rk ⇢ S, where values of ‘R’ are equals 0 or 1 and value of ‘k’ is non negative Integer is known as Boolean function.
Now we will see the Boolean operators.
There are three types of Boolean op...Read More