# Sets

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A is a set of all letters in the alphabet and B is a set of vowels in the alphabet. What kind of relationship exists between the two sets? Also, if C is the set of consonants what is the relationship between B and C?

• Sets -

B + C = A <~~Right?

A - B = C <~~??

What else can you come up with?

• Sets -

A is a set of all letters in the alphabet and B is a set of vowels in the alphabet. What kind of relationship exists between the two sets? Also, if C is the set of consonants what is the relationship between B and C?

The relationship between set A and B are that all B is a subset of A?
The relationship between B and C are when B and C unite they equal set A...right?

• Sets -

Yes, both of those are correct.

• Sets -

Remember correct grammar, though! "The relationship between set A and B is that..." ("Relationship" is the singular subject; therefore, the verb needs to be "is" not "are.")

• Sets -

A⊃B : A is a superset of B
B∩C = ∅ : the intersection of B and C is an empty set.

Note the difference:
"B is a set of vowels", and
"C is the set of consonants"

So B may or may not contain all the vowels.

That makes
B∪C ⊆ A : The union of B and C is a subset or equal to A.

In the case of:
"B is the set of vowels in the alphabet" means that B contains all the vowels, then
A = B∪C