INTRODUCTION TO LOGIC. PURPOSE: – To distinguish good arguments from poor ones Arguments consist of STATEMENTS – A statement is a sentence that can be.

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Presentation transcript:

INTRODUCTION TO LOGIC

PURPOSE: – To distinguish good arguments from poor ones Arguments consist of STATEMENTS – A statement is a sentence that can be declared either true or false – Statements can be either simple or compound

EXAMPLES OF STATEMENTS SIMPLE: Mrs. J teaches logic. COMPOUND: It is raining but it is warm. NOT STATEMENTS: – Get out a laptop. – Aren’t we having a great time? – Dan Marino was the best quarterback of all time.

COMPOUND STATEMENTS Formed by combining 2 or more simple statements that are separated by connectives CONNECTIVESYMBOLTRANSLATION Conjunction Λ..And..,..but also.. Disjunction VEither…or…. Negation ~ Not…, it is not the case that… Conditional/ Implication → If….then…., ….implies…. Bi-conditional ↔ ….if and only if…..

TRANSLATING COMPOUND SENTENCES Let A : Katie is a girl. Let B : Ducks swim. Let C : It is Tuesday. Let D : The sun is shining. Convert into English sentences: 1.~ B 2.A V B 3.C → D 4.~A Λ C 5.B → (C V D) 6.~D → (A Λ C)

Convert each statement into symbols. 1.Katie is a girl and it is not Tuesday. 2.If ducks swim then the sun is shining. 3.If both it is Tuesday and the sun is shining then ducks swim. 4.Katie is not a girl and ducks do not swim. 5.It is not the case that both it is Tuesday and the sun is shining. 6.It is not the case that either Katie is a girl or it is Tuesday.