HW1 solution - Math 2534 Solution to Worksheet 1 on Logic...

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Math 2534 Solution to Worksheet 1 on Logic Sp 2010 1) Given the following statements below: P: May goes hiking Q: Moose are on the trail R: It is raining Part A: Convert the following sentences into symbolic logic form. a) May goes hiking and it is raining. PQ b) May goes hiking but it is not true that moose are on the trail c) The following statement is not true. Moose are not on the trail but May does not go hiking. () Q P QP ≡∨  By De Morgan’s Law d) It is sunny or May does not go hiking. RP e) Either it is raining or Moose are on the trail. RQ Part B: Convert the following symbolic logic into a natural conversational English sentence. a) P ∧∨ It is raining and the moose are on the trail, or May is not hiking. b) By DeMorgan’s law we have: May is not hiking or Moose are not on the trail c) Q PQ ∨∧ by Absorption law we have: Moose are on the trail. 3) Using truth tables, verify the following; (Use a detailed and labeled truth table) a) ( )( )( ) w st ws wt ∧∨= ∧∨ ∧ b) w wt w ∧ ∨= c) kh k h ∨= ∧ a) SEE NEXT PAGE
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( ) ( )( ) w s t stw st wswt ws wt TTT T T T T T TTF T T T F T TFT T T F T T TFF F F F F F FTF T F F F F FFT T F F F F FTT T F F F F FFF F F F F F ∧∨ ∧∨ ∧ Since column 5 and column 8 have the same truth values we know that our conjecture is true and ( )( ) w st ws wt ∧∨= ∧∨ ∧ Part b) and c) use the same procedure as in part a) 4) Use DeMorgan’s law to find the negation of each of the following sentences.
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This note was uploaded on 01/28/2010 for the course MATH 2534 taught by Professor Mpmcquain during the Spring '07 term at Virginia Tech.

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HW1 solution - Math 2534 Solution to Worksheet 1 on Logic...

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