Truth table
Often show all possibilities true false pattern for statements
A truth table is a table used in logic to indicate the truth or falsity of a statement or proposition for every possible combination of input values. It is a tool used to determine the validity of a logical expression, and it provides a systematic way of evaluating complex statements.
The table consists of columns for every input variable and one column for the output. The output can either be true or false. The rows of the table represent all possible combinations of the input variables. The truth values determined by the input variable combinations are listed in the table below the respective input variables. Each combination of truth values corresponds to a row in the table.
Here is an example of a truth table for a basic logic statement involving two input variables, P and Q:
P | Q | P AND Q |
–|—|———|
0 | 0 | 0 |
0 | 1 | 0 |
1 | 0 | 0 |
1 | 1 | 1 |
In this example, P and Q can each be either true (1) or false (0). The column P AND Q represents the logical operator ‘AND’. The ‘AND’ operator returns true only if both operands are true. As we can see from the table, the only combination of input values that results in a true output is when P and Q are both true.
Truth tables are used to simplify complex logical expressions and determine the valid/invalid statements. They are also useful in digital electronics to analyze the behavior of logic gates and circuits.
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