We have seen prepositions, connectives and compound prepositions; all possible combinations of truth values of the individual prepositions in a compound preposition is depicted in a truth-table. However, it is possible that another preposition or compound preposition has the same truth values in the truth table. This is called logical equivalence of two prepositions. The …
In the previous video, you learned about different types of basic logical connectives that helps in creating compound prepositions. These connectives are join two or more atomic statements to form compound preposition which also have a truth value of its own. We have discuss negation, conjunction, and disjunction connectives so far, the remaining two connectives …
Prepositional Logic-Implication and Biconditional Read More »
From the previous article, you know that a prepositional statement can have truth value and the values are boolean – true or false. A statement having true value can be negated using ‘not‘ operator and then its value becomes false or vice-versa. Consider the following example where variable p is the statement “I am eating“. …
Prepositional Logic is kind of logic that studies “Statements” and derives relationship among those statements. What is a statement or a preposition ? When we talk we make many sentences but all sentences are not ‘Statements”. A sentence qualify as a statement when it has a truth value. There is only two truth value for …
Hasse Diagram is created for POSET or Partially Ordered Set. It means that there is a set of elements in which certain element are ordered, sequenced or arranged in some way. It is usually denoted as ≤, this is not “Less than, Equal to”, this symbol shows that elements are ordered. Now, there is a …
Permutation is arrangement of n objects taken r at a time. You keep arranging them by taken r number of objects at a time or take n objects at a time. Consider 4 objects – A , B ,C, D and 2 places 1 ,2, 3 . How many way can you arrange it? A …
A set of element S with binary operation * is semi-group if two of the property is satisfied 1. Since, S is a set with binary operation, it should satisfy closure property. i,e., a,b ∈ S, then a * b ∈ S 2. It must satisfy associative property. i.e., …
Preposition Logic and Problems
In the previous post , we learned about the prepositional statements and truth tables. You can visit the first post by clicking here. Tautology Formal definition of Tautology, “It is a statement which is True for all it’s variable values”. Meaning, It is a compound statement and each of it’s variable has a truth value …
Logical statements have truth values such as true or false. One or more simple logical statements can be connected to make a compound statement which also has truth value. The connectives are logical operators that connect one or more logical statements or atomic statements. The outcome depends on the truth value of individual statements that …
