homework 1 - Chapter 1, Section 1 1. Which of the following...

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Chapter 1, Section 1 1. Which of the following are statements? (I also discuss the truth value, where applicable) a) The moon is made of green cheese. YES (false) b) He is certainly a tall man. YES (it depends on who the man is) c) Two is a prime number YES (true) d) Will the game ever be seen? NO e) Next year interest rates will rise. YES (who knows about next year?) f) Next year interest rates will fall. YES (who knows about next year?) g) x 2 – 4 = 0 YES (true) 2. Given the truth values A true, B false, and C true, what is the truth value of each of the following wff's? a) A ( B C ) [T (F T)] [T T] T b) ( A B ) C [(T F) T] [F T] T c) ( A B )' C [(T F)' T] [F’ T] [T T] T d) A ' ( B ' C )' [T' (F' T)'] [F (T T)'] [F T'] [F F] F 3. What is the truth value of each of the following statements? a) 8 is even or 6 is odd T F true b) 8 is even and 6 is odd T F false c) 8 is odd or 6 is odd F F false d) 8 is odd and 6 is odd F F false e) If 8 is odd, then 6 is odd F Æ F true f) If 8 is even, then 6 is odd T Æ F false g) If 8 is odd, then 6 is even F Æ T true h) If 8 is odd and 6 is even, then 8 < 6 (F T) Æ F true 4. Find the antecedent and consequent in each of the following statements. a) Healthy plant growth follows from sufficient water. antecedent: sufficient water consequent: healthy plant growth b) Increased availability of information is a necessary condition for further technological advances. antecedent: further technological advances consequent: increased availability of information c) Errors will be introduced only if there is a modification of the program. antecedent: errors will be introduced consequent: there is a modification of the program d) Fuel savings implies good insulation or storm windows throughout. antecedent: fuel savings consequent: good insulation or storm windows throughout 5. Negate the following statements: a) The answer is two or three 1. Neither two nor three is the answer. 3. The answer is not 2 and it is not 3. b) Cucumbers are green and seedy. 2. Cucumbers are not green or not seedy. c) 2 < 7 and 3 is odd. 4. 2 7 or 3 is even.
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6. Write the negation of each statement a) If the food is good, then the service is excellent. F Æ S is F' S. Negated: (F' S)' is F S' The food is good, but the service is poor. b) Either the food is good or the service is excellent. F S. Negated: F' S' The food is poor and so is the service. c) Either the food is good and the service is excellent, or else the price is high (F S) P Negated: (F S)' P'. Either the food is poor or the service is poor, but the price is low. d) Neither the food is good nor the service is excellent. F' S' Negated: F S Either the food is good or the service is excellent.
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homework 1 - Chapter 1, Section 1 1. Which of the following...

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