# Problems from Complement of a set

Let $$A = \{a,e,i,o,u\}$$ and $$B = \{b,c,d,f,g,\ldots,z\}$$ be the sets of vowels and consonants of the alphabet.

a) What is the complementary of $$A$$?

b) And $$B$$?

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### Development:

We realize that sets $$A$$ and $$B$$ are, respectively, the vowels and the consonants of the alphabet. Therefore, we can easily answer the proposed questions.

a) The complement of $$A$$ is $$B$$ since the letters that are not vowels are consonants.

b) Reciprocally, the letters that are not consonant are vowels, since the letters of the alphabet can divided into consonants and vowels.

### Solution:

a) $$A^c=B$$

b) $$B^c=A$$

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