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Applied Mathematics for Database Professionals phần 2

Tất cả các quyền. Không có một phần của công việc này có thể được sao chép, truyền đi dưới bất kỳ hình thức nào hoặc bằng bất kỳ phương tiện, điện tử hoặc cơ khí, bao gồm cả photocopy, ghi âm, hoặc bằng bất kỳ lưu trữ thông tin hoặc hệ thống thu hồi, mà không có sự cho phép trước bằng văn bản của chủ sở hữu quyền tác giả và nhà xuất bản | CHAPTER 1 LOGIC INTRODUCTION 13 Table 1-5. Truth Table for AND Conjunction P Q P Ù Q T T T T F F F T F F F F P Ù Q is TRUE if and only if both P and Q are TRUE. In all other cases P Ù Q is FALSE. In a conjunction P Ù Q P and Q are referred to as the conjuncts. Table 1-6. Truth Table for OR Disjunction P Q P V Q T T T T F T F T T F F F P V Q is FALSE if and only if both P and Q are FALSE. In a disjunction P V Q P and Q are referred to as the disjuncts. Note The OR operator that is defined here is called the inclusive or. In natural language we normally refer to the inclusive or when using the word or. However we sometimes use or to denote what is called the exclusive or eor for short . Compared to the truth table for the inclusive or Table 1-6 the truth table for the exclusive or differs only on the first row the propositional form P eor Q is FALSE if both P and Q are TRUE. An example use of the exclusive or is in the statement You must clean up your room or you go to bed early. Clearly you aren t required to both clean up your room and go to bed early. In this book we will always use the inclusive or. Table 1-7. Truth Table for IF. THEN Implication P Q P Q T T T T F F F T T F F T 14 CHAPTER 1 LOGIC INTRODUCTION P Q is FALSE if and only if P is TRUE and Q is FALSE. In all other cases P Q is TRUE. In an implication P Q P is often referred to as the antecedent hypothesis or premise and Q as the consequent or conclusion. Table 1-8. Truth Table for IF AND ONLYIF Equivalence P Q P Q T T T T F F F T F F F T Logical equivalence is nothing more than the conventional operator as it applies to Boolean values P Q is TRUE if and only if P and Q have the same truth value. Another common way to express equivalence is to use the words necessary and sufficient. Note that the negation see Table 1-4 is a monadic operator it accepts only one operand. The other connectives in Tables 1-5 through 1-8 are dyadic they accept two operands. Note Other books sometimes use the terms unary .