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?
B + C = A <~~Right?
A - B = C <~~??
What else can you come up with?
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?
Yes, both of those are correct.
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.")
You can also add:
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
The relationship between set A (all letters in the alphabet) and set B (vowels in the alphabet) is that B is a subset of A. In other words, all elements of set B (vowels) are also elements of set A (all letters). However, set A contains elements that are not in set B (consonants).
Now, let's consider set C (consonants). The relationship between sets B and C is that they are complementary sets. In other words, all elements in set B (vowels) are not present in set C (consonants), and vice versa. The union of sets B and C will give you the original set A (all letters) since the vowels and consonants together make up all the letters in the alphabet.