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The logical product of two or more logical sum terms is known as a product of sums expression. POS is an ANDing of ORed variables. The boolean expression containing all the input variables either in complemented or un complemented form in each of the sum term is known as a canonical POS expression and each term is called maxterm. For example, express the product of sum from the boolean function F(X, Y) and the truth table for which is given below:

Now by multiplying max terms for the output 0’s, we get the desired product of sums expression which is (X+Y') (X’+Y).

The sentences which can be determined to be true or false are called truth function.

LHS: = (X+Y) (X+Z)
= XX + XZ + XY + YZ
= X + XZ + XY + YZ
= X + (1 + Z +Y) YZ
= X + YZ
= RHS

The result TRUE or FALSE of logical statement are called truth values.

Another name of Boolean algebra is ‘Switching Algebra’.

Idempotent law using truth table

1. a term (A) ANDed with an parenthetical expression (B+C) equals that term ANDed with each term within the parenthesis: A.(B+C) = AB+AC;

2. a term (A) ORed with a parenthetical expression (B . C) equals that term ORed with each term within the parenthesis: A+(BC) = (A+B) . (A+C).

The complementarity law states that a term ANDed with its complement equals 0, and a term ORed with its complement equals 1 (AA’ = 0, A+A’ = 1).

The commutative law states that the order in which terms are written does not affect their value. For example, (AB = BA, A+B = B+A).

When a variable combines with itself using OR or AND operator and produces the same variable as output is called idempotent law.

For example, X + X = X, X.X=X

This law states that the double complement of a variable gives the same variable.

Truth tables are a means of representing the results of a logic function using a table. They are constructed by defining all possible combinations of the inputs to a function and then calculating the output for each combination in turn.

The “NOT” is simply the opposite or complement of its original value.

A minterm is a special product of literals, in which each input variable appears exactly once.

A maxterm is a sum of literals, in which each input variable appears exactly once.

The OR is a disjunction operator and denotes logical addition.

The Logical AND operator is a conjunction operator and denotes logical multiplication.

The truth table for NOT operation.

It is a simple equality statement i.e., A(BC) = ABC or A+(B+C) = A+B+C.

The three logical operators are AND, OR and NOT.

The logic function is a compound statement that consists of a logic statement with logical operators like AND, OR and NOT.

The examples for logic functions are
X NOT Y OR Z
Y AND X OR Z

If the result of any logical statement or expression is always TRUE is called Tautology and the result of any logical statement is always FALSE is called fallacy.