Please explain the answer to the question 3
I don't understand why all complements are mutually exclusive. please give me the example. I think no mutually exclusive sets are complements.
Thank you for reaching out!
The example from the lecture explains why all complements are mutually exclusive.
Let the set of all ingers be our universal set (our sample space). Then, define the following two sets:
Set A - the set of all even numbers in the universal set
Set B - the set of all odd numbers in the universal set
Sets A and B are complements since
1) an integer is either even or odd
2) the union of A and B covers the entire sample space.
As a result of 1), sets A and B are also mutually exclusive - an integer cannot be both even and odd at the same time.
Therefore, complements are always mutually exclusive. Note, however, that, as stated in the lecture, this statement doesn't go both ways. This means that not all mutually exclusive sets are complements.
Hope this helps!