Logic:
Logic is a language for reasoning. Logic is a formal study of mathematics; it is the study of mathematic reasoning and proofs itself. Since logic can helps us to reason the mathematical models it needs some rules associated with logic so that we can apply those rules for mathematical reasoning. It helps us to understand how to construct a valid argument. There are lots of applications of logic in the field of computer science for e.g. designing circuits, programming, program verifications, etc.
Proposition:
Proposition is a declarative sentence (i.e. declaring a fact or stating an argument) that is either true or false, but not both. See the examples below:
2 + 2 = 5. (False),
It is hot today. (If it is hot then true)
Kathmandu is the capital of Nepal. (True)
All the above examples are either true or false. So, the given sentences are propositions.
Try to analyze the sentences below:
x > 5, Come here, Who are you?
The given sentences are not propositions since we cannot say whether they are true or false.
Propositions are denoted conventionally by using small letters like p, q, r, s …. The truth value of proposition is denoted by T for true proposition and F for false proposition. Reminder: p, q ,r ,s … are not actual propositions but they are propositional variables i.e. place holders for propositions. Variables that are used to represent propositions are called propositional variables.
Propositional Logic:
The logic that deals with propositions is called propositional logic or propositional calculus. It is the area of logic that studies ways of joining and/or modifying propositions to form more complicated propositions and it also studies the logical relationships and properties derived from these combined propositions. A propositional logic consists of propositions and connectives. The proposition are then connected by connectives, such as AND (∧), OR (∨), NOT (¬), implication (→), biconditional (↔).
Simple/Compound Proposition:
Any statement whose truth value doesn’t depend on another proposition is called simple proposition.
eg. Kathmandu is capital of Nepal.
Compound proposition is formed from simpler propositions and express relationship among the constituent statements.
eg. If you try hard for your exam, then you will succeed.