Table 7 logical equivalences involving conditional statements. This is a theorem in the book but it is not proved, so we. Pdf mathematical logic and logical equivalence implementation. Start studying logical equivalences involving conditional statements. To understand why this table is the way it is, consider the following example. Predicates can be obtained by removing some or all nouns from a statement. The term logical equivalence law is new to us, but in fact, we already. The truth or falsity of a statement built with these connective depends on the truth or falsity of its components. The statement p is called the hypothesis of the implication, and. Logical equivalence is different from material equivalence.
Two possibly compound logical propositions are logically equivalent if they. Rule statement equivalent statement 1 if p then q not p or q 2 if p then q q or not p 3 if p then q if not q then not p examples statement equivalent statement a if it is blue, then it is the sky. Lets now demonstrate this equivalency a different way by using the established laws of equivalence. Conditional and biconditional logical equivalencies rot5. In logic, predicates can be obtained by removing some or all of the nouns from a statement.
Conditional propositions and logical equivalence section 1. Propositional logic, truth tables, and predicate logic. A statement in sentential logic is built from simple statements using the logical connectives. If p, then q is called an implication or a conditional.1478 457 121 112 1593 1293 867 753 1002 547 1415 756 55 351 373 731 938 1198 716 1591 516 1568 1275 371 132 851 921 477 805 1394 470 593 174 405 245 922 785 1496 1135 12 982 673 1389 1353 1117