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.