6. [8 marks] Snow and the Students A frustrated student wrote the following statements on a piece of paper, which was then crumpled into a ball: If the city of Vancouver owns only one snowplow, then 10cm of snow will be sufficient to cause chaos. If the city of Vancouver owns multiple snowplows, then it will raise taxes by 7%. If people in the lower mainland know how to drive in the snow, then UBC will remain open. If the city of Vancouver decided to install a high-tech otter detection system in the Sun Yat-Sen garden, then it owns only one snowplow. Either 10cm of snow will not be sufficient to cause chaos, or UBC will be closed for the day, or possibly both. Either CPSC 121 labs are cancelled, or people in the lower mainland know how to drive in the snow, or both. If the city of Vancouver raises taxes by 7%, then it will install a high-tech otter detection system in the Sun Yat-Sen garden. a. [2 marks Rewrite each of these statements using propositional logic. Make sure to define the propositions you are using. That is, state something like: "s: the city of Vancouver owns only one snowplow" before writing a proposition involving s. As stated on piazza, assume that the city of Vancouver owns at least one snowplow, so the statement The city of Vancouver owns only one snowplow is the negation of the statement The city of Vancouver owns multiple snowplows. b. (6 marks Using your answer from part (a), known logical equivalences, and the rules of inference, determine whether or not CPSC 121 labs are cancelled. 6. [8 marks] Snow and the Students A frustrated student wrote the following statements on a piece of paper, which was then crumpled into a ball: If the city of Vancouver owns only one snowplow, then 10cm of snow will be sufficient to cause chaos. If the city of Vancouver owns multiple snowplows, then it will raise taxes by 7%. If people in the lower mainland know how to drive in the snow, then UBC will remain open. If the city of Vancouver decided to install a high-tech otter detection system in the Sun Yat-Sen garden, then it owns only one snowplow. Either 10cm of snow will not be sufficient to cause chaos, or UBC will be closed for the day, or possibly both. Either CPSC 121 labs are cancelled, or people in the lower mainland know how to drive in the snow, or both. If the city of Vancouver raises taxes by 7%, then it will install a high-tech otter detection system in the Sun Yat-Sen garden. a. [2 marks Rewrite each of these statements using propositional logic. Make sure to define the propositions you are using. That is, state something like: "s: the city of Vancouver owns only one snowplow" before writing a proposition involving s. As stated on piazza, assume that the city of Vancouver owns at least one snowplow, so the statement The city of Vancouver owns only one snowplow is the negation of the statement The city of Vancouver owns multiple snowplows. b. (6 marks Using your answer from part (a), known logical equivalences, and the rules of inference, determine whether or not CPSC 121 labs are cancelled
