QR Question (union)

[ysurge19]

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3. For which of the following could set {-100, -50, -25, 25, 50, 100} satisfy G ∪ F?

• A. F = {x ≥ 100}, G = {x ≤ -100}
• B. F = {|100|}, G = {-50, -25}
• C. F = {x < 100}, G = {x < -100}
• D. F = {x < 25}, G = {x < -25}
• E. F = {x ≥ 14}, G = {x ≤ -14}

To solve this problem, we need to find F and G that are satisfied by the given set of numbers. Since the union of G and F means that the numbers in the set must satisfy G, F, or both, we can eliminate the choices that do not satisfy either one.

Choice A:

-50, -25, 25, and 50 do not satisfy either F or G, this answer choice is incorrect.

Choice B:

-100, 50, and 25 do not satisfy either F or G, this answer choice is incorrect.



OK so that is the question and some of the answer. Math is my weak point so I have no idea how they are getting those numbers under Choice A and Choice B (in explanation)...

can someone explain how they went about attempting choice A to get that data set?

I do kind of know what a union and intersection is.

Thanks for your time

 

[DMikes]

A Union means that the set must satisfy EITHER G OR F OR BOTH. It truly is a broad swath. The answers in Choice A are all from the data set provided (-100, -50, -25, 25, 50, 100). The answer picks out those values (-50, -25, 25, and 50) because they don't fall under F or G. For example, -50 is neither greater than or equal to 100 nor is it less than or equal to -100. Thus, since it does not satisfy either G or F, nor does it satisfy both, it cannot be the answer. The same explanation can be given for choice B. I assume the correct answer is E as it's the only one that can account for every number in the set. (Unless I'm missing something obvious)


Essentially, go through every number in the provided set and confirm that it can be accommodated by either F, G, or both for each answer choice.


If you're still confused or have more questions, feel free to DM me!