Question

What is truth table and its significance?

Answer 1

Truth table:

1. The truth table is a type of mathematical table which gives the necessary breakdown of the logical function by listing all the possible values that the function will attain.
2. A truth table is a kind of chart which is used to determine the true values of propositions and the exact validity of their resulting argument.
3. For example, a very basic truth table would simply be the truth value of a proposition p and its negation, or opposite, not p (denoted by the symbol ∼ or ⇁ ).
4. Such a table typically contains several rows and columns, with the top row representing the logical variables and combinations, in increasing complexity leading up to the final function.

Significance:

1. The truth table of logic gates gives us all the information about the combination of inputs and their corresponding output for the logic operation.
2. The great advantage of the Shortened Truth Table Technique is that it can be used to prove either validity or invalidity -just like any truth table.
3. Therefore -unlike formal proofs- this technique can prove both the validity and the invalidity of arguments.
4. A logic gate truth table shows each possible input combination to the gate or circuit with the resultant output depending upon the combination of these input(s).

Thus, a truth table is a mathematical table that gives the breakdown of the logical functions.