Practice - Question 6
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
List three integers in the set S that are divisible by 5 but not by 7.
💡 Hint: Think about multiples of 5.
Is the set of all integers countable or uncountable?
💡 Hint: Can you list all integers?
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
Is the set of integers divisible by 5 but not by 7 countable?
💡 Hint: Remember the process of listing integers.
What is the main characteristic of the decimal representation in the discussed set of real numbers?
💡 Hint: Recall what digits are in the decimal representations.
Get performance evaluation
Challenge Problems
Push your limits with advanced challenges
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.
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.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.