Basic set theory question
Reading an olympiad combinatorics book. Is there an error with this question?
Prove that Union(A,B) is the smallest set that contains both A and B.
My ideas:
By definition Intersection(A,B) subset of Union(A,B)
Since Intersection(A,B) is greatest set that contains both A and B, shouldn't Union(A,B) be greatest set?
Prove that Union(A,B) is the smallest set that contains both A and B.
My ideas:
By definition Intersection(A,B) subset of Union(A,B)
Since Intersection(A,B) is greatest set that contains both A and B, shouldn't Union(A,B) be greatest set?
Original post by asianism
Reading an olympiad combinatorics book. Is there an error with this question?
Prove that Union(A,B) is the smallest set that contains both A and B.
My ideas:
By definition Intersection(A,B) subset of Union(A,B)
Since Intersection(A,B) is greatest set that contains both A and B, shouldn't Union(A,B) be greatest set?
Prove that Union(A,B) is the smallest set that contains both A and B.
My ideas:
By definition Intersection(A,B) subset of Union(A,B)
Since Intersection(A,B) is greatest set that contains both A and B, shouldn't Union(A,B) be greatest set?
"C contains A and B" means that every element of A is in C and every element of B is in C.
It does *not* mean "every element x that is a member of both A and B is an element of C".
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