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If A = {2,4,6,8,10} B = {1,3,5,7,9} X or U = N {1,2,3,...}

Find:

  • Ac ∩ Bc
  • Ac - Bc
  • (A ∩ B)c

Since the compliment set of A is all the elements of the Universal set that are non-existent in A, and the Universal set in this example is equal to natural numbers (infinite), how do i list all the numbers, is there a specific way to do this or do i just write it as Ac = {1,3,5,7,9,11,..}

Thanks,

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    You might find it a little easier if you first apply identities to the first and second ones (specifically, De Morgan's) to simplify it a bit. This should give you sets that are a bit nicer to describe. – 2017-02-18

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In general, you can use set-builder notation. For instance, the complement of $\{3,4,5\}$ can be written

$$ \{ x \in \mathbb{N} \mid x < 3\} \cup \{x \in \mathbb{N} \mid x > 5 \} \enspace. $$

There are many variations on this notation, but the main idea is to define a set by the properties satisfied by its elements. These properties are specified by formulae like $x \leq 10$ or $x = 2n+1$ for $n \in \mathbb{N}$ (to specify odd natural numbers).