CS F214 – LOGIC IN COMPUTER SCIENCE – TUTORIAL – 1 – Reasoning Skills
1. Given the following statements, identify the conclusion in each case from the options provided
a. Statements :
If the train arrives late and there are no taxis at the station, then John is late for his meeting. John is not late
for his meeting. The train did arrive late.
Conclusion?
i) Therefore, there were no taxis at the station
ii) Therefore, there were taxis at the station.
Answer:
b. Statements:
If it is raining and Jane does not have her umbrella with her, then she will get wet. Jane is not wet. It is
raining.
Conclusion
i) Therefore, Jane has her umbrella with her.
ii) Therefore, Jane does not have her umbrella with her.
Answer:
2. If you're a fitness walker, there is no need for a commute to a health club. Your neighborhood can be
your health club. You don't need a lot of fancy equipment to get a good workout either. All you need is
a well-designed pair of athletic shoes.
This paragraph best supports the statement that
a. fitness walking is a better form of exercise than weight lifting.
b. a membership in a health club is a poor investment.
c. walking outdoors provides a better workout than walking indoors.
d. fitness walking is a convenient and valuable form of exercise.
e. poorly designed athletic shoes can cause major foot injuries.
Ans:
3. In the past, consumers would rarely walk into an ice cream store and order low-fat ice cream. But that
isn't the case today. An increasing health consciousness combined with a much bigger selection of tasty
low-fat foods in all categories has made low-fat ice cream a very profitable item for ice cream store
owners.
This paragraph best supports the statement that
a. low-fat ice cream produces more revenue than other low-fat foods.
b. ice cream store owners would be better off carrying only low-fat ice cream.
c. ice cream store owners no longer think that low-fat ice cream is an unpopular item.
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d. low-fat ice cream is more popular than other kinds of ice cream
e. consumers are fickle and it is impossible to please them
Ans:
4. For the sentences, list the propositional variables and the declarative sentences.
Also convert into propositional logic statements, using the connectives.
a. I will only go to school if I get a chocolate now.
b. Ram or Sita is good
c. Ram and Sita is good
d. If the sun shines today, then it won’t shine tomorrow.
e. If the barometer falls, then either it will rain or it will snow.
f. Today it will rain or shine, but not both.
5. For the paragraph given below, List the prosositional variable and the declarative sentences. Write the
propositional formulas, and sequent.
a. 1.a, 1.b.
b. Michale is coming to the trip. If Michale comes then Mark also comes. If Michale and Mark both
come then Ryan will not come. Therefor Ryan will come.
6. Prove using Natural Deduction. (Assume AND introduction and AND elimination rules)
a. (𝑝 ∧ 𝑞) ∧ 𝑟, 𝑠 ∧ 𝑡 ⊢ 𝑞 ∧ 𝑠
b. 𝑝 ∧ 𝑞 ⊢ 𝑞 ∧ 𝑝
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