Practice Question Number 11 (14.1.6) - Lecture -14 - Discrete Mathematics

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6 sample questions

Question 1.
What is an irrational number?
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Think about definitions involving fractions.
Question 2.
Can you give an example of an irrational number?
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Consider numbers that can't be precisely written as fraction.
3Question 3.
What is a key feature of irrational numbers?
- They can be expressed as fractions.
- They cannot be expressed as fractions.
- They are always negative.
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Consider their definitions closely.
4Question 4.
True or False: √2 can be expressed as a ratio of two integers.
- True
- False
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Think about previous discussions regarding numbers.
Question 5.
Prove using induction based on parity that the sum of any two odd integers is even.
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Focus on the properties of odd integers.
Question 6.
Using strong induction, show that if √n is irrational for n=2, it remains true for any integers beyond that.
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Revisit the structure of your proof for clarity.

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