In mathematics, generally a truth table is used to demonstrate the relation between Boolean function and propositional Calculus. In other words, truth table is a type of mathematical table that is used in logic for defining the truth value of a statement formula for each possible Combination of values taken by their logical variables. Now we will see how to make a truth table. Truth table consists of rows and columns. In truth table column entries are given for input variables. For a given statement or any expression having ‘x’ distinct components would have ‘2n’ rows in its truth table. Two truth values, 'true' and 'false' are denoted by symbol ‘T’ and ‘F’ respectively (or in binary notation sometimes also denoted as 1 and 0).
In truth table the Logical disjunction or logical alternation is a compound sentence that is obtained by using the word ‘or’ which means to join two simple sentences.
Suppose the value of one operand is true then result we find is also true. And if the values of both operands are false, then the result we get will also be false or the result will be true if at least one of its operands is true.
Symbolically, the truth table for S OR P can be written as S v P or S + P. Now we will discuss how to define Truth Tables.
S v P truth table for disjunction function:
S P S v P
T T T
T F T
F T T
F F F
Now we will see the truth table for negation function:
The truth table of negation is given as:
If we put value of 'S' as True then we get the negation of 'S' as false. And if we put the value of 'S' as false then we get the negation of 'S' as true. This is all about truth tables.