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 -

    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

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