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Logic ChAPTER 3

Logic ChAPTER 3. Statements 3.1. A statement is a declarative sentence that can be classified as true or false but not both simultaneously. A statement is either simple or compound. Statement. 1. Boston is the capital of Massachusetts. . 2. Lemons and oranges are citrus fruits.

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Logic ChAPTER 3

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  1. LogicChAPTER 3

  2. Statements3.1

  3. A statement is a declarative sentence that can be classified as true or false but not both simultaneously. A statement is either simple or compound. Statement

  4. 1. Boston is the capital of Massachusetts.. 2. Lemons and oranges are citrus fruits. 3. Jane is taking English and she has four themes to write. 4. Do you like mathematics? 5. Walk a mile. Examples Simple Statement Compound Statement Compound Statement Not a Statement Not a Statement

  5. Conjunction If two statements are combined by the word and (or an equivalent word such as but),the resulting statement is called a conjunction. The conjunction is symbolized by pΛq.

  6. If two statements are combined by the word or,the resulting statement is called a disjunction. The disjunction is symbolized by pvq. Disjunction

  7. Write each statement in symbolic form using the indicated letters to represent the corresponding components. a. This is April (a), and income tax returns must be filed (f). b. Violets are blue (b), but roses are pink (p). c. I will take art (a) or music (m) next term. Examples

  8. The negation of a given statement is a statement that is false whenever the given statement is true and true whenever the given statement is false. The negation of a statement is denoted by ~p. Negation

  9. Let p be “Robin can type” and let q be “Robin takes shorthand.” Write each statement in symbolic form. Robin can neither type nor take shorthand. It is not the case that Robin can type and take shorthand. Examples

  10. De Morgan’s Law For any statement p and q, means and means

  11. Examples Given: p: Ricky loves Lucy q: Lucy loves Ricky Give a verbal translation of each statement. It is not true that Ricky or Lucy love each other. Ricky does not love Lucy and Lucy does not love Ricky. It is not the case that Ricky and Lucy love each other. Ricky does not love Lucy nor does Lucy love Ricky.

  12. Quantifiers Statement Negation All a’s are b’s. Some a’sare not b’s. No a’s are b’s. Some a’sare b’s. All No (none) Negations Negations Some are not. (There is one.) Some are. To help you remember how to negate statements, use this diagram.

  13. Examples Give the negation of each statement. All men are mortal. Some men are not mortal. Some women are teachers. No women are teachers. Some things are not what they appear to be. All things are what they appear to be. Somebody up there loves me. END Nobody up there loves me.

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