Last answered:

22 Jan 2021

Posted on:

10 Jan 2021


Why even numbers and Prime numbers are considered complements?

In the quiz of

Mutually Exclusive Sets

lesson Even numbers and prime numbers were considered complements, why?
2 answers ( 0 marked as helpful)
Posted on:

21 Jan 2021



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.

Posted on:

22 Jan 2021


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

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