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Why even numbers and Prime numbers are considered complements?

Why even numbers and Prime numbers are considered complements?

Super Learner
0
Votes
2
Answer

In the quiz of

Mutually Exclusive Sets

lesson
Even numbers and prime numbers were considered complements, why?

2 Answers

Super Learner

Hi,

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
0
Votes

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.

Best,
365 Vik