Practice Question 6 (9.1.6) - Tutorial 5 - Discrete Mathematics

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6 sample questions

Question 1.
List three integers in the set S that are divisible by 5 but not by 7.
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Think about multiples of 5.
Question 2.
Is the set of all integers countable or uncountable?
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Can you list all integers?
3Question 3.
Is the set of integers divisible by 5 but not by 7 countable?
- True
- False
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Remember the process of listing integers.
4Question 4.
What is the main characteristic of the decimal representation in the discussed set of real numbers?
- Contains only 1s
- Contains all digits
- Contains only 0s
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Recall what digits are in the decimal representations.
Question 5.
Consider a set of integers having certain divisibility conditions. Formulate a proof to show that the set of integers divisible by both 3 and 5 but excluding multiples of 10 is countable.
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Start by outlining the integers that meet your criteria.
Question 6.
Define a custom set involving real numbers with decimal representations consisting of 0s and 1s. Prove whether this new set is countable.
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Look for patterns in finite binary representations.

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