Tautology - Equivalences Rules:

If there Tautologies are not all the time as much easy to note as the one above so than we can use these truth tables to be definite that a statement we have written is true, that is regardless of the truth of the individual propositions it contains. Just to do same this, the columns of our truth table will be headed with more over larger sections of the sentence, if there until the final column contains the entire sentence. So as we seen as before, that the rows of the truth table will represent all the possible models for the sentence, that is- each possible assignment of truth values to the single propositions in the sentence. So we will use these initial truth values to assign truth values to the subsentences in the truth table, rather other then use these new truth values to assign truth values to larger subsentences and possible so on. But, if the final column in the entire sentence is usually assigned true, so it means that there, at anything the truth values of the propositions being discussed, thus the whole sentence will turn out to be true.

If there we see that there in seventh and eighth columns -  the truth values that have been built up from the earlier columns - have accurately the same truth values in each row. It sense that our sentence is made up of the two sub sentences in these columns, because of that our overall equivalence must be correct. So the truth of this statement demonstrates that the connectives →and ^are related by a property is known as  distributivity, that we come back to later on.