# Question 3 on Complements

after viewing the video https://learn.365datascience.com/courses/probability/complements

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?

thanks

- 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.
- 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)
- Negative numbers and non-negative numbers -->Now , Their Union forms entire Universe of Numbers