PHIL2642: Critical Thinking
Practice Exercises on Conditionals and Deduction Questions only in this document
1 (i) State the necessary and sufficient condition of each of these conditional claims. Rewrite the claims in the form of “If … then …”.
(ii) Give an example of something which would be a counterexample to each of these claims. If a counterexample is impossible, say why.
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a) Every spider has venom.
b) You won’t die of lung cancer if you don’t smoke.
c) Only people who aren’t Muslims drink alcohol.
d) All voters in Australian federal elections are people over 18 years old.
e) It is only Melbournians who don’t like Sydney.
f) If volunteer fire-fighters were paid by the Government it would put too much strain on the budget.
g) Only if Australia accepts more refugees will we not be internationally criticised.
h) It’s not an episode of Keeping Up with the Kardashians if it doesn’t have numerous meaningful pauses.
i) Only if it’s black and chewy is it liquorice.
j) All people who are working legally in Australia have a tax file number.
2) State the necessary and sufficient conditions for the conditional claim in these arguments. What is the form of each of the arguments? Is this a valid form or an invalid form?
a) If you contribute at your job you’ll be appreciated. You did contribute, so you will be appreciated.
b) If you are irritating me I can’t be held responsible for what I do. You are not irritating me, so I can be held responsible for what I do.
c) If a dog isn’t trained from when it’s a puppy, it not be a well behaved adult. Sandy is a very well behaved dog, so he must have been trained from when he was a puppy.
d) Spot is a dog, and since only human beings are moral agents, Spot can’t be a moral agent.
e) All members of the household buy groceries, but John isn’t a member of the household. Therefore John doesn’t buy any groceries.
f) Only those who are not vegetarian eat meat. John eats meat, so he is not a vegetarian.
g) Sonia did not pass the exam. Since everyone who did not study did not pass, we can conclude that she did not study.
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