Proposition:
A proposition is a statement which is either true or false but not both. For example, 9<10 (true) is proposition; 4+9=14 is a proposition (false). The truthfulness or falsity of the proposition is called truth value of the proposition. If a proposition is true, then its truth value is denoted by T and if it is false then its truth value is denoted by F.
Logical connectives and compound propositions:
Usually we combine any two propositions by means of the phrases and, or, if then, if and only if. These are called the logical connectives and the propositions which are involved with the logical connectives are called the compound propositions. A proposition with out any connectives is called a simple proposition.
Example:
a) If you work hard then you pass the exam.
b) I like Math and my brother likes Science.
Conjunction:
It is a compound proposition whose components are connected by the word and. If p and q are any two simple propositions then the p and q is denoted by p^q. p^q is true only when both p and q are true. Otherwise it is false.
Disjunction:
It is a compound proposition whose components are connected by the word or. If p and q are any two simple propositions then the p or q is denoted by pvq. pvq is true only when either p or q are true. i.e. pvq is false only when both p and q are false.
Conditional statement:
It is a compound proposition whose components are connected by the phrase if then. If p and q are any two simple propositions then the if p then q is denoted by pàq. pàq is true only when p is true and q is false. Otherwise it is false.
Biconditional statement:
It is a compound proposition whose components are connected by the phrase if and only if . If p and q are any two simple propositions then the if p if and only if q is denoted by p↔q. p↔q is true only when p and q have the same truth values. Otherwise it is false.
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