Practice Cartesian Product Of The Integers (4.2.1) - Module No # 05 - Discrete Mathematics

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6 sample questions

Question 1.
What is a countable set?
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Think of sets that can be listed.
Question 2.
Give an example of a Cartesian product of two finite sets.
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Consider pairing elements.
3Question 3.
Is there an infinite number of pairs in ℤ × ℤ?
- True
- False
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Consider how many integers exist.
4Question 4.
How does the enumeration process of ℤ × ℤ begin?
- (0
- 0)
- (1
- 1)
- (1
- 0)
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Remember where we start counting from.
Question 5.
Design a method to prove that the Cartesian product of two countably infinite sets is also countably infinite.
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Think about combining the sequences without omitting any element.
Question 6.
How would you determine the 15th pair in the enumeration of ℤ × ℤ?
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Examine the systematic pattern in listing pairs.

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