Which of the following sets are equal? (Select all that apply.) [selections on description below]

Question

A = {3, 4, 5}

B = {x  R| 2 ≤ x < 6}

C = {x  R| 2 < x < 6}

D = {x  Z| 2 < x < 6}

E = {x  Z⁺| 2 < x < 6}

Answer 1

Hello Louis!

To determine which sets are equal, let's determine what is in each set, exactly. The first set, A, is already laid out for us. We are given that A = {3, 4, 5} which is as simple as we can have.

So then, what elements are in B? Every set other than A is written in set builder notation. So, the first part of B says "x  R". This section tells us what numbers are candidates to exist in the set B. Thus every real number will be considered as a possible element of the set B. The second portion of the set notation tells us exactly which elements of the real numbers, determined in the previous step, are in the set. It says "2 ≤ x < 6". Thus a real number is in B if and only if it is greater than or equal 2 and less than 6. In summary, {x  R| 2 ≤ x < 6} tells us that B is the set of all real numbers x such that x is greater than or equal to 2 and less than 6. Therefore, we have that B = [2, 6), which is every element between 2 and 6 along with 2 itself.

Now that we have determined what elements are in B, each remaining set will be determined similarly. I will leave the rest for you to solve. Some tips:

1. When considering C, notice that the only difference between this set and B is that in B the real number 2 is included whereas 2 is not included in C.
2. D and E have the same restrictions as C, but consider different types of numbers as possible elements than C. Specifically, D considers the integers and E considers the positive integers.

Good luck!