9.4. Set of Integers Divisible by 5 but not by 7

Try these first

1. 1.

   List three integers that belong to the set S.

   Hint

   Think of multiples of 5.

2. 2.

   What is the first positive integer in set S?

   Hint

   It's the smallest multiple of 5.

3. 3.

   Which of the following integers is in set S?

   • 0
   • 35
   • 14

   Hint

   Look for the multiples of 5 that do not involve 7.

4. 4.

   Is the set S countably infinite?

   • True
   • False

   Hint

   Consider how many terms can be sequenced.

5. 5.

   Show how to enumerate the first 50 elements of set S.

   Hint

   Start from zero and count up and down in 5s, skipping those divisible by 7.

6. 6.

   Determine if the subset of the set S consisting of positive integers is still infinite.

   Hint

   Reflect on the pattern established from the multiples.