B tech. Discrete mathematics (I. T & Comp. Science Engg.) Syllabus

Biconditional Statement: Let P and Q be propositions.The biconditional statement P  Q ^{is the proposition} "P ^{if and only if} Q"^. The biconditional statement is true when P and Q have same truth values and is false otherwise.

Biconditional statements are also called bi-implications. It is also read as p is necessary and sufficient condition for Q.

The truth table for biconditional statement is as follows.

P	Q	P  Q
T T F F	T F T F	T F F T

Example 7 : Let P : Ram can take the flight. Q : Ram buy a ticket.

Then P  Q is the statement.

“Ram can take the flight iff Ram buy a ticket”.
Precedence of Logical Operators:

We can c o n s t r u c t c o m p o u n d p r o p o s i t i o n s u s i n g t h e n e g a t i o n operator and the logical operators defined so far. We will generally use parentheses to specify the order in which logical operators in a compound proposition are to be applied. In order to avoid an excessive number of parentheses.

We sometimes adopt an order of precedence for the logical connectives. The following table displays the precedence levels of the logical operators.