Question

Use set builder notation to express the set of all positive integer multiples of five greater than 5 and less than 100.

Select the correct answer below:
O p∈Z and 1<5p<20
O 5p
O 5p
O {5p|p∈Z and 1

Answer 1

The correct answer is option 3. The set builder notation for all positive integer multiples of five greater than 5 and less than 100 is 5p .

Step-by-step explanation:

To represent the set of all positive integer multiples of five that are greater than 5 and less than 100 using set builder notation, consider the following:

• The smallest positive multiple of five greater than 5 is 10 (2 × 5).
• The largest positive multiple of five less than 100 is 95 (19 × 5).
• Each multiple can be represented as 5p, where p is a positive integer.
• The set includes all positive integers p for which 5p is between 10 and 95.

So the set builder notation that represents this set is p ∈ Z and 1 < p < 20 because when p is 2, 5p = 10 and when p is 19, 5p = 95.

Comparing with the provided options, the correct one is 5p because it correctly captures all integer multiples of five that fall within the specified range.