Problems from Union and intersection of sets

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

a) What is their intersection?

b) And their union?

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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) There is no letter that is both, consonant and vowel, therefore, the intersection of these two sets is empty.

b) The union is the whole set of letters of the alphabet.

Solution:

a) $A \cap B = \emptyset$

b) $A \cup B = U$ , where $U$ is the universal set that in this case is the alphabet.

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