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Truth Tables

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Truth tables are used for the description of data according to the different values. In digital electronics truth table are used as the Basic Terms to explain boolean algebra and Logic gates. In short truth table is used to explain the logic basically in the connection with the Boolean algebra, Boolean Functions and propositional Calculus.
Understanding truth tables is not difficult, the explanation is shown below:
A truth table has one column for each input variable and the result is shown in the last column for all the possible results of logical operation for which a table is designed. One possible configuration of input variables is denoted by the rows of truth table.
Some terms are necessary for understanding the truth tables. The first concept is logical identity and logical negation.
Logical identity is an operation on one logical value that gets the value true if the operand is true and a false value if the operand is false.
The logical negotiation is an operation on the logical values and the operand is true if the operand is false.
Logical conjunction is an operation on two values that is the value of two propositions; the result produces a value true if both the operands are true.
Logical disjunction is an operation of two propositions that gives the result true if at least one of its operands is true.
Logical implication is an operation of two propositions that shows the value is false in case the first operand is true and the second operand is false.
Logical equality is known as bi conditional and is an operation of two propositions that shows the value is true if either both operands are true or false.
Logical NAND is an operation of two propositions that shows the value is false if both the operands show the value true. One of its operands must be false to make the value true.

Define Truth Table

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A truth table is used to find the relation with Boolean Algebra, Boolean function and propositional Calculus. In other word, we can say that it is a type of mathematical table which is used in logic for showing the truth value of a statement formula for each possible Combination of values taken by their logical variables.
Now, let’s see how you can Define Truth Tables. As we know that a truth table is consist of columns and rows. In the truth table the columns are defined for input variables and results of the logical operation for expression we want to represent. For a statement or any expression having ‘x’ distinct components would have ‘2n’ rows in its truth table. Two truth values, 'true' and 'false' are represented by symbol ‘T’ and ‘F’ respectively (or sometimes also denoted by binary symbols 1 and 0).
In the truth table the Logical disjunction or logical alternation is a compound sentence which is formed by using the word ‘or’ to join two simple sentences.
If the value of one operand is true then result will also be true. If the values of both operands are false, then the result will also be false or we can say that that result will be true if at least one of its operands is true.
Symbolically, the truth table for X OR Y is written as X v Y or X + Y.
Now we will see how to Define Truth Tables.
x v y truth table for disjunction:

x y x v y
T T T
T F T
F T T
F F F

In the above statements ‘X’ is false and the statement ‘Y’ is true.
Truth table for given statements:


X

Y

X v Y
F T T
The disjunction for the given statements is true. This is all about truth table.