conditional proposition]

If p and q are two propositions, then the compound proposition, "if p then q" is known as conditional statement or implication. It is denoted by p q. p is called the antecedent (or hypothesis). q is called the consequent (or conclusion). Note: p q can be read as (..

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..

Summary - A Boolean algebra is a set B with two distinct elements, along with the binary operations '+' and '.' and a unary operation (') which satisfy closure property, commutative property, existence of unit element, distributive property for both the binary operations. Moreover, for all x B, the..

If both p and q have the truth value F, p q has the truth value T(F F = T). It should be noted that in the above example, the simple statement p and q depend on each other. In other words, if the truth value of one depends on the truth value of the other and p q is true, then the conditi..

Arguments and their Validity - A compound proposition is a tautology if it is always true for all possible combination of the truth values of its components. If a compound proposition which is always false for all possible combination of the truth values, of its components then ..