Question

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

a. p∈Z and 1<5p<20
b. 5p
c. 5p
d. {5p|p∈Z and 1

Answer 1

The set of all positive integer multiples of five between 5 and 100 is expressed in set builder notation, which corresponds to Option b.

Step-by-step explanation:

We are tasked with using set builder notation to express the set of all positive integer multiples of five that are greater than 5 and less than 100.

To do this, we first recognize that a positive integer multiple of five can be represented as 5p, where p is a positive integer. Since we need multiples greater than 5 and less than 100, p must be greater than 1 (because 5 x 1 = 5) and less than 20 (because 5 x 20 = 100). Therefore, our condition for p is 1 < p < 20.

Now, placing it within set builder notation, we represent the set as where represents the set of all integers. This notation describes a set that includes all numbers of the form 5p, with p being an integer strictly between 1 and 20.