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Why even numbers and Prime numbers are considered complements?

Why even numbers and Prime numbers are considered complements?

Super Learner

In the quiz of

Mutually Exclusive Sets

Even numbers and prime numbers were considered complements, why?

2 Answers

Super Learner


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.

365 Team

Hey M.S.M,

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.

365 Vik