Practice Lecture No#38 (17.3) - Module No#08 - Discrete Mathematics

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6 sample questions

Question 1.
List the possible pairs of integers from 1 to 8 that sum to 9.
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Look for pairs where one number increases and the other decreases.
Question 2.
What is the midpoint formula for two points (x1, y1) and (x2, y2)?
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Think about averaging the coordinates.
3Question 3.
What does the pigeonhole principle guarantee in the context of distinct points?
- A. At least one point will be repeated
- B. At least one pair of points will have integer midpoints
- C. All points will have integer coordinates
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Think about how points can be categorized.
4Question 4.
Choosing 5 integers from 1 to 8 always results in what?
- True
- False
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Consider the defined pairs available.
Question 5.
Consider the integers from 1 to 15. Prove that choosing any 8 integers guarantees a pair that sums to 16.
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How many pairs can you make from the given integers?
Question 6.
Construct a proof showing that for any integer n, a number constructed with n 1s is divisible by n.
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Explore numbers like 1, 11, 111, and analyze their remainders.

5 more questions in this section. Enroll free to practise them all.