In the quiz of
Mutually Exclusive Sets
Even numbers and prime numbers were considered complements, why?
By definition, a complement of an event/set is everything the event/set is not. Defining our sets as:
- A = All even numbers
- B = All prime numbers (all numbers that can only be divided by 1 and themselves)
- A’ = All odd numbers
- B’ = All composite numbers (all numbers that can not only be divided by 1 and themselves)
A and B are not complements because their intersection is not the empty set. There is a value which is both even and prime, 2.
The answer “prime numbers and even numbers” isn’t incorrect because they’re compliments, but because they aren’t mutually exclusive. As Jacobo has noted, the number 2 is simultaneously even and prime, which makes this answer incorrect.
The correct one is ending in a draw or winning a game, since you can’t do both at the same time, but you can also lose a game, which means they aren’t complements.