Practice Tutorial 2: Part Ii (14.1.2) - Lecture -14 - Discrete Mathematics

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6 sample questions

Question 1.
What is the relationship between arithmetic mean and geometric mean for two numbers?
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Think about how averages work.
Question 2.
Can you represent the number 6 as a sum of distinct powers of two?
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Consider the binary equivalent.
3Question 3.
The arithmetic mean of two positive numbers is always:
- Less than their geometric mean
- Equal to their geometric mean
- Greater than or equal to their geometric mean
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Think about the two numbers in question.
4Question 4.
True or False: Every integer has a distinct binary representation.
- True
- False
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Consider how binary digits work.
Question 5.
Using your understanding of the AM-GM inequality, prove that for any three positive numbers, the arithmetic mean will always be greater than the geometric mean.
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Start by proving for two, then extend your logic.
Question 6.
Create a logical argument or a proof for how many guests can be at a party where everyone is not a celebrity.
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Think about the implications of 'knowing' someone.

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