The following logic problems involve translating between English and “Logic”.
For each problem.
a) Identify the universal class. (What do all the terms refer to?)
b) Extract the terms and assign letters to each of them.
c) Restate each of the statements in symbolic form.
d) Find the chain of implication and use it to obtain the conclusion.
e) State this conclusion in English.

Problem 1:
i. Liars cannot be trusted.
ii. Carnivores are very clever.
iii. A man who tells the truth is admirable.
iv. No vegetarians are zookeepers.
v. One can always trust a very clever person.
Note: Assume that the negation of vegetarian is carnivore.
Problem 2:
i. No tiger ever doubts that he is handsome.
ii. An animal, that cannot whistle, is not worth listening to.
iii. No animal is quite certain that it is handsome, unless it has a shiny
coat.
iv. All animals, except tigers, respect their parents.
v. No aquatic animal can whistle.
vi. An animal with a shiny coat is worth listening to.

A strategy game.
Alice and Bob attend a charity auction and decide to bid on the same item, a headband
worn by the lead guitarist of their favourite, but not very successful, band.
The rules of the auction are as follows:
• • Alice and Bob make alternating bids. Nobody else is interested in the headband.
• • The bid must be higher than the last bid by $10, $20 or $50. We start at $0.
• • Alice or Bob are unwilling to pay more than $100, so whoever bids $100 wins. We can think of the auction as being a strategy game.
a) Draw a state graph representing this game. Specify your notation for the
graph carefully.
b) Bob lets Alice go first. Making an appropriate assumption, who wins?
c) How many different combinations of legal bids adding to $100 are there,
what are they, and how does this relate to the state graph?
d) Consider that either Alice or Bob, but not both at the same time, has only
$20 notes and has to make bids of $20. Assume the other doesn’t know they
only have $20 notes. Does either situation change the result?