Description

Write your own description of what a truth table is and what it can be used for.

what a truth table is:

            What? + General Uses

                        Intro:

A truth table is a tabular representation of the truth values of propositional variables and compound propositions. It is used in logic; particularly in propositional calculus, Boolean algebra, and Boolean functions. It is a breakdown of all possible truth value outcomes a given compound proposition can attain. Such outcomes are based on all possible truth value combinations of the propositional variables that make up the given compound proposition, hence the name truth table.

                        Describe: Structure:

A truth table usually contains multiple rows and columns. The table has one column for each propositional variable; p, and q for example. Followed by columns representing each constituent compound proposition that a logical connective has been applied to; increasing in complexity leading up to the final compound proposition in the last right most column. The number of rows of the truth table is determined by the number of propositional variables that make up the compound proposition. The number of rows is equal to 2 to the power of the number prepositional variables. For instance, if we had three propositions p, q, and r, there would be 8 rows. This is done to guarantee that there are enough rows to cover all possible truth value combinations. Each row of the truth table contains one possible combination of the truth values of propositional variables; for instance, T(p)=0, T(q)=1, and T(r)=0. The resulting truth value of the final compound proposition that is based on these true values is represented at the end of the same row.

                        Describe: General USES:

A truth table can be used as a way of organizing complex compound propositions, and list out the outcome of all possible scenarios. Consequently, it can be used as a tool to better visualize whether an argument or a complex proposition is true for all legitimate truth values, that is, logically valid. furthermore, truth tables are used to check if a certain compound proposition is either a tautology, or consistent, or a contradiction. Truth tables may also be used to check whether or not two compound propositions are equivalent; based on the outcome of their respective truth tables. Moreover, in Boolean algebra, truth tables can be used to reduce basic Boolean operations to simple correlations of inputs and outputs with out need for logic gates or code. For example, an adder for binary addition can be represented with a truth table. Additionally, truth tables synergize with Boolean algebra; where both are used by engineers to produce the simplest possible circuit that will perform desired logic function. Which improves efficiency and cuts costs.

Constructing truth tables by oneself is considerably useful, yet this has limitations. Notably, compound propositions can be made up with many propositional variables. For instance, if a compound propositions has 10 different propositional variables; then its truth table will have 1024 rows. Building such truth table by oneself is strenuous and tedious. Luckily, computers can be leveraged to generate truth tables for highly complex logic functions.

                        Limitations:

Some functions have many input variables, and consist of many constituent functions. This can result in a table with hundreds of rows and columns. Computers are used to generate truth tables for highly complex logic functions.

Truth tables are usually used for logic problems as in Boolean algebra and electronic circuits.

- In digital electronics and computer science (fields of applied logic engineering and mathematics), truth tables can be used to reduce basic Boolean operations to simple correlations           of inputs to outputs, without the use of logic gates or code. For example, a             binary addition can      be represented with the truth table.

- Computers are used to generate truth table for highly complex logic function. The truth     table     works hand in hand with Boolean algebra, of which it is used by engineers to       find the            simplest           possible circuit that will perform desired logic function

                        -Link to Boolean Algebra and Theorems/Axiams, and K-maps and forming simplest                                    expressions for efficient practical circuits.

            -An alternative to the truth table is the use of Boolean theorems. This method, called            Boolean algebra, is used by engineers to find the simplest possible circuit that will      perform a desired logic function. This optimizes system efficiency by minimizing the   number            of operations that must be performed to accomplish a given task.”       

                        -ie. With addition of Boolean algebra, Boolean methods can be applied to find the                            simplest possible circuit that will perform a desired logic function.  This optimizes                            system efficiency by minimizing the number of operations that          must be performed to                           accomplish a given task.

-A truth table is a way of organizing information to list out all possible scenarios.

            The truth table contains the truth values that would occur under the premises of a given        scenario. As a          result, the table helps visualize whether an argument is logical (true) in the scenario.

            -Truth tables can be used to show whether a propositional expression is true for all   legitimate input values, that is, logically valid.-Truth tables can be used to show whether a