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CHAPTER 2 THE LOGIC OF

COMPOUND

STATEMENTSTHE LOGIC OF

COMPOUND

STATEMENTS

Equivalence

SECTION 2.1

3 The central concept of deductive logic is the concept of argument form. An argument is a sequence of statements aimed at demonstrating the truth of an assertion. The assertion at the end of the sequence is called the conclusion, and the preceding statements are called premises. To have confidence in the conclusion that you draw from an argument, you must be sure that the premises are acceptable on their own merits or follow from other statements that are known to be true.Logical Form and Logical Equivalence 4 Fill in the blanks below so that argument (b) has the same form as argument (a). Then represent the common form of the arguments using letters to stand for component sentences.

a.If Jane is a math major or Jane is a computer science major, then Jane will take Math 150. Jane is a computerscience major. Therefore, Jane will take Math 150.

b.If logic is easy or , then .

I will study hard.

Therefore, I will get an A in this course.

Example 1 -Identifying Logical Form

5 Example 1 -Solution1. I (will) study hard.2. I will get an A in this course.

Common form: If por q, thenr.

Therefore, r.

Statements

7 StatementsMost of the definitions of formal logic have been developed so that they agree with the natural or intuitive logic used by people who have been educated to think clearly and use language carefully. The differences that exist between formal and intuitive logic are necessary to avoid ambiguity and obtain consistency. In any mathematical theory, new terms are defined by using those that have been previously defined. However, this process has to start somewhere. A few initial terms necessarily remain undefined. 8 StatementsIn logic, the words sentence, true, and falseare the initial undefined terms. 9

Compound Statements

10 Compound StatementsWe now introduce three symbols that are used to build more complicated logical expressions out of simpler ones. The symbol ~ denotes not, ????denotes and, and ????denotes or. Given a statement p, the sentence "~p" is read "not p" or "It is not the case that p" and is called the negation of p. In some computer languages the symbol ????is used in place of ~. 11 Compound StatementsGiven another statement q, the sentence "p????q" is read "pand q" and is called the conjunction of pand q. The sentence "p????q" is read "por q" and is called the disjunction of pand q. In expressions that include the symbol ~ as well as ????or ????, the order of operations specifies that ~ is performed first.

For instance, ~p????q= (~p) ????q.

12 Compound StatementsIn logical expressions, as in ordinary algebraic expressions, the order of operations can be overridden through the use of parentheses. Thus ~(p????q) represents the negation of the conjunction of pand q. In this, as in most treatments of logic, the symbols ????and ???? are considered coequal in order of operation, and an expression such as p????q????ris considered ambiguous. This expression must be written as either (p????q) ????rorquotesdbs_dbs3.pdfusesText_6

[PDF] [PDF] THE LOGIC OF COMPOUND STATEMENTS THE LOGIC OF

[PDF] Chapter 2: The Logic of Compound Statements 21: Logical - USNA