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Question 3 on Complements

Question 3 on Complements


after viewing the video https://365datascience.teachable.com/courses/506102/lectures/9302986
if i understand correctly a complement, is everything you do not want the outcome to be.
In question 3/3 of the module, it asks:
Which of these are complements? (in order to answer this, do we not first need to know what the favourable outcome is? as this is not stated)
Aside from this, if i then consider each of the options to answer:

  • Positive and negative numbers (these are opposites)
  • Non-negative and non-positive numbers (these are opposites)
  • Positive numbers and non-negative numbers (these are the same thing)
  • Negative numbers and non-negative numbers (these are opposites)

So given we have three answers that are one type and one answer that is another type, how is the given answer ‘Negative numbers and non-negative numbers’ deemed to be a complement, given it is the same type as two of the others?
please can you explain or offer some further insight to explain how the this answer is reached, especially when it is not stated in the question what the favourable outcome is?

2 Answers


Hi Folk,
Let Me explain this question.
See When We say Positive Numbers We does not include 0 but all Numbers greater than 0.
When We say Negative Numbers  We does not include 0 but all Numbers less than 0.
Positive Union {0} = Non-Negative Numbers
Negative Union {0} = Non-Positive Numbers

  1. Non-negative and non-positive numbers –> 0 is in the intersection, complements says to be disjoint thus, they are not as their is an intersection therefore , not a complement.
  2. Positive and negative numbers –> It looks that they are opposite but their union does not form entire Universe since , 0 is left behind(We know that A + comp of A should form entire Universe)
  3. Negative numbers and non-negative numbers –>Now , Their Union forms entire Universe of Numbers

         Negative Numbers= Less than 0 …..   Non Negative O and all Greater than 0 ===So Enitre Real numbers we got.
         Negative Numbers= Less than 0 …..   Non Negative O Interesction all Greater than 0 ===So Empty Set or Disjoint Set.
 Now You know the answer 🙂
I hope i am clear

thank you for taking the time to answer, regrettably it is still not clear to me from your answer how option 3 is considered the right answer to this question. Further given the detailed answer you have provided, I am unsure how, as a student of the course I am expected to know the answer as, unless i have completed missed it, the concepts of non-negative numbers and such is not covered in any of the videos or Course note PDFs? If anyone else is able to add further insight or explanation, this would be appreciated. Thanks again for your time in offering an initial answer.

9 months

365 Team

Hey Daniel, 
This one’s on me. I wanted to sneak in a trick question and see whether students can distinguish between non-negative and positive (and non-positive and negative). 
So, the idea is that complements need to 1) cover the entire sample space and 2) not overlap. 
Positive and negative break rule 1), because they don’t include 0. 
Non-negative and non-positive break rule 2), because they overlap. 
Positive and non-negative break both rule 1) and 2) because they don’t include any negative numbers, but all positive numbers overlap. 
Hence, the right answer is negative and non-negative. 
365 Vik

that takes some getting your head around! in other words if i understand correctly and subsequently work to the principle, Zero is not a positive number but it is a non-negative or non-positive number, then I should understand this better going forward. thanks for taking the time to explain.

9 months