Practice Schroder-bernstein Theorem (4.3.2) - Module No # 05 - Discrete Mathematics

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6 sample questions

Question 1.
What is an injective function?
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Think of a one-to-one relationship.
Question 2.
Does the function f(x) = x^2 is injective for positive integers?
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Check if any two inputs lead to the same output.
3Question 3.
What does the Schroder-Bernstein theorem establish about the cardinalities of sets?
- They can never be equal
- They are equal if both have injective functions
- They are always infinite
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Think back to the conditions required for the theorem.
4Question 4.
True or False: If |A| ≤ |B|, it necessarily means A is larger than B.
- True
- False
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Refer to the definition of cardinality.
Question 5.
Prove that the set of all rational numbers is countably infinite using the concepts from the Schroder-Bernstein theorem.
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Use the structured nature of rational numbers to establish your mappings.
Question 6.
Show two sets, one infinite and one finite, and explain how this relates to the application of the Schroder-Bernstein theorem.
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Consider graphing both sets to visualize the relationships.

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