example of biconditional proposition

A statement of something to be done or considered is called proposition. You are familiar with statements such as If two straight lines intersect each other then the vertically opposite angles are equal. The angles opposite to equal sides of a triangle are equal. Proposition is..

Conditional and Biconditional Statements - It is already mentioned in earlier classes that compound statements of different propositions can be obtained by conjunction, disjunction and negation of propositions. We just recall these three basic logical connectivities an..

Logical Equivalence - Two propositions (simple or compound) are said to be logically equivalent if they have identical truth values. If p is logically equivalent to q, we denote p q. We have already constructed the truth table of (~p) q in earlier class. Recall the same truth table. Truth..

If two simple statements p and q are connected by the connective 'if and only if', then the resulting compound statement is called the biconditional statement. Symbolically it is represented by p q. Example: An integer is even if and only if it is divisible by 2. It is a ..

If two simple statements p and q are connected by the connective 'if and only if', then the resulting compound statement is called the biconditional statemen..

Proposition or statement and Truth Value of a statement - A declarative sentence which is true or false but not both is called a proposition..

q is false only when p is true and q is false. In other cases, it is true. If p q, then the contrapositive of this proposition is -q -p. The biconditional p q is true only when both p and q are true or both p and q are false. A compound proposition which is always true ..

If p and q are propositions, then the conjunction of conditionals p q and q p is called a biconditional proposition. Let us construct the truth table of (p q) (q p) The last column of above table is identical to the last column of earlier table..

Propositions are usually denoted by p, q, r, s et..

Let p be any proposition. The proposition "not p" is called the negation of p. It is denoted by ~p. [The negation of p is false if p is true and the negation of p is true if p is false] Following is the truth table for ~p..