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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
List three integers in the set S that are divisible by 5 but not by 7.
💡 Hint: Think about multiples of 5.
Question 2
Easy
Is the set of all integers countable or uncountable?
💡 Hint: Can you list all integers?
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
Is the set of integers divisible by 5 but not by 7 countable?
- True
- False
💡 Hint: Remember the process of listing integers.
Question 2
What is the main characteristic of the decimal representation in the discussed set of real numbers?
- Contains only 1s
- Contains all digits
- Contains only 0s
💡 Hint: Recall what digits are in the decimal representations.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider a set of integers having certain divisibility conditions. Formulate a proof to show that the set of integers divisible by both 3 and 5 but excluding multiples of 10 is countable.
💡 Hint: Start by outlining the integers that meet your criteria.
Question 2
Define a custom set involving real numbers with decimal representations consisting of 0s and 1s. Prove whether this new set is countable.
💡 Hint: Look for patterns in finite binary representations.
Challenge and get performance evaluation