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Logic

Logic. a statement is a sentence that is either true or false. Statement: Compound statement:. a statement that contains one or more simpler statement (not, and, or, if . . . then, only if, if and only if). Determine which of the following are statements.

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Logic

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  1. Logic

  2. a statement is a sentence that is either true or false • Statement: • Compound statement: a statement that contains one or more simpler statement (not, and, or, if . . . then, only if, if and only if)

  3. Determine which of the following are statements. 2. Solve the equation 2x + 5 = 3. 3. x2 + 1 = 0 has no solution.

  4. Connectives • Negation: • Conjunction: • Disjunction: • Conditional: denial of a statement (symbol: ~) and (symbol: ^) or – inclusive or (symbol: V) if . . ., then (symbol: →)

  5. Using the symbolic representationsp: The car costs $40,000.q: The car goes 140 miles per hour.r: The car is red.express the following compound statements in symbolic form. The car is red, goes 140 mph, and does not cost $40,000.

  6. Using the symbolic representationsp: I am an environmentalist.q: I recycle my aluminum cans.r: I recycle my newspapers.express the following compound statements in symbolic form.

  7. Negation F T

  8. Conjunction T F F F

  9. Disjunction T T T F

  10. Conditional T F T T

  11. Construct a truth table for:

  12. DeMorgan’s Laws

  13. Conditionals

  14. Write the converse, inverse, and contrapositive of the sentence: If you do not eat meat, you are a vegetarian Converse: If you are a vegetarian, then you do not eat meat. Inverse: If you do eat meat, then you are not a vegetarian. Contrapositive: If you are not a vegetarian, then you do eat meat.

  15. The Dragons of Lidd There are two types of dragons in the Kingdom of Lidd. Rational dragons, being sensible, have determined that devouring farm animals and their owners is, in the long run, not healthy for dragons. Predator dragons, on the other hand, respond to their instincts and refuse to do otherwise, nor do they show any fear of humans. Dragons in Lidd are also of two different colors related to their veracity. Red rational dragons always tell the truth, and red predator dragons always lie. Grey rational dragons always tell the truth and grey predator dragons always lie. Because dragons are few in number and are considered an endangered species, the King has decreed that rational dragons shall be protected, and that any knight caught slaying a rational dragon will be dealt with severely. It would help to know which dragons are rationals and which are predators. It would also help to know a dragon’s color. (If one catches a red dragon in a lie, one would know that he is a predator.) Unfortunately, there is an affliction endemic to humans in Lidd: they are colorblind. To them, all dragons look grey.

  16. The Dragons of Lidd One Dragon For this dragon’s statement, construct a truth table. Then explain how to interpret in word each row of the table. Dragon: I am a grey predator.

  17. The Dragons of Lidd Another Dragon For this dragon’s statement, construct a truth table. Then explain how to interpret in word each row of the table. Dragon: I am not a red rational.

  18. The Dragons of Lidd Wishy-Washy Dragons For this dragon’s statement, construct a truth table. Then explain how to interpret in word each row of the table. Dragon A: I am either red or I am rational.

  19. The Dragons of Lidd Forthright Dragons For this dragon’s statement, construct a truth table. Then explain how to interpret in word each row of the table. Dragon A: If I am rational, then I am red.

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