Conditional and Biconditional statements

A conditional statement is a statement which is performed by if true or false. For eg: if p and q are two propositions, "if p then q" is known as conditional statement or implication. A statement is called biconditional when it is expresses the idea that the presence of some property is a necessary and sufficient condition for the presence of some other property.

Conditional and Biconditional Statements:

Conditional statements and biconditional statements of different propositions may be obtained by conjunction, disjunction and negation of propositions.

Conjunction Statement:
If p and q are two propositions, then compound proposition, "p and q" is known as conjunction of the proposition. It is indicated by p q. The conjunction of two propositions p and q are true, if both p and q are true and in all other cases it is false.

Disjunction Statement:
If p and q are two propositions, then the compound proposition "p or q" is called the disjunction of p and q. It is indicated by p v q. The disjunction p v q of two proposition p and q are false if both p and q are false and in all other cases, it is true.

Negation Statement:
Let p be any proposition. The suggestion "not p" is called the negation of p. It is indicated by ~p. The negation p is false if p is true and also the negation p is true if p is false.

Example for Conditional and Biconditional Statements:

Consider the proposition, “If it is rainy then it is cloudy”, which we say is a conditional statement.
Let us consider, p =“It is raining”, q =“It is cloudy”. Then the proposition can be written as “If p then q”. We symbolize this as, p à q. This can also be deliberated as “p implies q”. We never want something false to follow from something true; i.e. we do not want “If pq” to be true if p is not true and then q is not true.