Discrete Mathematics: Propositional Logic Introduction | Predicate Logic

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• published: 19 Mar 2015
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propositional logic examples, first order logic, hindi, predicate logic, propositional logic tutorial, propositional logic exercises, propositional logic truth tables, propositional logic symbols Conjunction The joining of two or more propositions by the word "and" results in their so-called conjunction or logical product; the propositions joined in this manner are called the members of the conjunction or the factors of the logical product. The conjunction, "p and q", has truth for its truth-value when p and q are both true; Otherwise it has falsehood for its truth-value. Formally, If p and q are proposition variables, the conjunction of p and q is a compound proposition "p and q." We symbolize the logical conjunction of p and q by p q. It is true when, and only when, both p and q are true. If either p or q is false, or if both are false, p q is false. Equivalently, If p and q are true, then p q is true; otherwise p q is false. The truth values for conjunction (or equivalently, the truth table for the operator ) are depicted in a following table. p q p q T T T T F F F T F F F F There are other English conjunction that have the same logical meaning as "and," although their psychological content may be differ. Famous examples are "but" and "however." Some additional examples are "moreover," "nevertheless," and "in addition to which." Whatever the verbalization may be, we symbolize the logical conjunction of p and q by p q. 3. Disjunction The joining of two or more propositions by the word "or" results in their so-called disjunction or logical sum; the propositions joined in this manner are called the members of the disjunction or the summands of the logical sum. The disjunction, "p or q", has truth for its truth-value when p is true and also when q is true, but if falsehood when both p and q are false.Formally, If p and q are proposition variables, the disjunction of p and q is "p or q" and we symbolize the logical disjunction of p and q by p q. It is true when at least one of p or q is true and is false only when both p and q are false. Equivalently, If p and q are false, then p q is false; otherwise p q is true. The truth values for disjunction (or equivalently, the truth table for the operator ) are depicted in a following table. p q p q T T T T F F F T F F F F In logic, we avoid possible ambiguity about the meaning of the word "or" by understanding it to mean the inclusive "and/or." In logic, we generally used "or" in the nonexclusive sense. For instance, to say "x is rational or it is negative" does not mean that it cannot be both rational and negative. We shall use consistently the interpretation that at least one of the choices must hold, and both may be hold. 4. Incompatibility Russell defines incompatibility as the proposition whose truth-value is truth when p is false and likewise when q is false; its truth-value is falsehood when p and q are both true. We symbolize the logical incompatibility of p and q by p | q. Accordingly, the table for the operator | is shown in the following table. p q p | q T T F T F T F T T F F T Note that incompatibility is also the disjunction of the negation of p and q i.e. "~p or ~q." Propositional Form A propositional form (or statement form) is an expression made up of sententials (statement variables) such as p, q, and r, and sentential operators (or logical connectives) such as ~, , , that becomes a sentential formula (or statement) when actual statements are substituted for the compound statement variable. The truth table for a given statement propositional form displays the truth values that correspond to the different combinations of truth values for the sentential variables. As an example, construct the truth table for propositional form (p q) ~(p q). As we have said, when "or" is used in its exclusive sense, the statement "p or q" means "p or q but not both" or "p or q and not both p and q" which translate into (p q) ~(p q) and this sometimes abbreviated (p q) or (p XOR q) depending upon the context. p q p q p q ~(p q) (p q) ~(p q) T T T T F F T F T F T T F T T F T T F F F F T F lecture 1 propositional logic propositional logic examples 1 categorical vs propositional logic propositional logic tutorial propositional logic formulas basics propositional logic propositional logic tutorial pdf propositional logic problems propositional logic examples first order logic predicate logic propositional logic pdf propositional logic tutorial propositional logic exercises propositional logic truth tables propositional logic symbols propositional logic exercises and solutions propositional logic problems proposition examples propositional logic examples pdf propositional logic tutorial propositional logic exercises predicate logic examples propositional logic examples in ai

Discrete Mathematics: Propositional Logic Introduction | Predicate Logic

• Report rights infringement
• published: 19 Mar 2015
• views: 39197

propositional logic examples, first order logic, hindi, predicate logic, propositional logic tutorial, propositional logic exercises, propositional logic truth tables, propositional logic symbols Conjunction The joining of two or more propositions by the word "and" results in their so-called conjunction or logical product; the propositions joined in this manner are called the members of the conjunction or the factors of the logical product. The conjunction, "p and q", has truth for its truth-value when p and q are both true; Otherwise it has falsehood for its truth-value. Formally, If p and q are proposition variables, the conjunction of p and q is a compound proposition "p and q." We symbolize the logical conjunction of p and q by p q. It is true when, and only when, both p and q are true. If either p or q is false, or if both are false, p q is false. Equivalently, If p and q are true, then p q is true; otherwise p q is false. The truth values for conjunction (or equivalently, the truth table for the operator ) are depicted in a following table. p q p q T T T T F F F T F F F F There are other English conjunction that have the same logical meaning as "and," although their psychological content may be differ. Famous examples are "but" and "however." Some additional examples are "moreover," "nevertheless," and "in addition to which." Whatever the verbalization may be, we symbolize the logical conjunction of p and q by p q. 3. Disjunction The joining of two or more propositions by the word "or" results in their so-called disjunction or logical sum; the propositions joined in this manner are called the members of the disjunction or the summands of the logical sum. The disjunction, "p or q", has truth for its truth-value when p is true and also when q is true, but if falsehood when both p and q are false.Formally, If p and q are proposition variables, the disjunction of p and q is "p or q" and we symbolize the logical disjunction of p and q by p q. It is true when at least one of p or q is true and is false only when both p and q are false. Equivalently, If p and q are false, then p q is false; otherwise p q is true. The truth values for disjunction (or equivalently, the truth table for the operator ) are depicted in a following table. p q p q T T T T F F F T F F F F In logic, we avoid possible ambiguity about the meaning of the word "or" by understanding it to mean the inclusive "and/or." In logic, we generally used "or" in the nonexclusive sense. For instance, to say "x is rational or it is negative" does not mean that it cannot be both rational and negative. We shall use consistently the interpretation that at least one of the choices must hold, and both may be hold. 4. Incompatibility Russell defines incompatibility as the proposition whose truth-value is truth when p is false and likewise when q is false; its truth-value is falsehood when p and q are both true. We symbolize the logical incompatibility of p and q by p | q. Accordingly, the table for the operator | is shown in the following table. p q p | q T T F T F T F T T F F T Note that incompatibility is also the disjunction of the negation of p and q i.e. "~p or ~q." Propositional Form A propositional form (or statement form) is an expression made up of sententials (statement variables) such as p, q, and r, and sentential operators (or logical connectives) such as ~, , , that becomes a sentential formula (or statement) when actual statements are substituted for the compound statement variable. The truth table for a given statement propositional form displays the truth values that correspond to the different combinations of truth values for the sentential variables. As an example, construct the truth table for propositional form (p q) ~(p q). As we have said, when "or" is used in its exclusive sense, the statement "p or q" means "p or q but not both" or "p or q and not both p and q" which translate into (p q) ~(p q) and this sometimes abbreviated (p q) or (p XOR q) depending upon the context. p q p q p q ~(p q) (p q) ~(p q) T T T T F F T F T F T T F T T F T T F F F F T F lecture 1 propositional logic propositional logic examples 1 categorical vs propositional logic propositional logic tutorial propositional logic formulas basics propositional logic propositional logic tutorial pdf propositional logic problems propositional logic examples first order logic predicate logic propositional logic pdf propositional logic tutorial propositional logic exercises propositional logic truth tables propositional logic symbols propositional logic exercises and solutions propositional logic problems proposition examples propositional logic examples pdf propositional logic tutorial propositional logic exercises predicate logic examples propositional logic examples in ai