compound proposition

Normally propositions are joined by 'OR', 'AND', 'NOT', 'IF .. THEN..' and 'IF AND ONLY IF' called the logical connectives . They are symbolised as follows: If two or more statements are combined by the use of words like 'AND', 'OR', 'IF AND ONLY IF ', then the resulting statement is ..

Suppose a compound proposition is given, we first split it into simple propositions containing a single connective. Using the rules discussed above, we construct the truth table in the form of columns and the last column gives the truth value of the given proposi..

Logical Equivalence and Duality - Two compound propositions p and q are said to be logically equivalent, if their truth values are same for each different combinations of the truth values of the components involved in them. If p and q are logically equivalent, then it is represe..

Two compound propositions p and q are said to be logically equivalent, if their truth values are same for each different combinations of the truth values of the components involved in them. If p and q are logically equivalent, then it is represented by p ..

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..

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..

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 it is calle..

If p and q are two propositions, the compound proposition "p or q" is called the disjunction of p and q. It is denoted by p q. [The disjunction p q of two proposition p and q are false if both p and q are false and in all other cases, it is true] The tru..

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 Table fo..