# A Historical Event

What historical event does the following rebus represent? $$\therefore \forall A, B: (A \cap B = \emptyset) \implies (A \neq B)$$

Hint:

$\forall x \in S, \text{ where } |S| = 9.$ This isn't a rebus, but it describes one aspect of the event.

• I believe it is $LaTeX$ rebus, not math haha. May 20, 2016 at 20:11
• this is false, let $A=B=\emptyset$
– JMP
May 20, 2016 at 20:53
• Your hint is not a fully formed mathematical statement.
– Deusovi
May 20, 2016 at 21:57
• @Deusovi I know, unfortunately. Couldn't think of a better way to state it. May 20, 2016 at 21:59
• @Leppy: It's "an" if you don't pronounce the H. Some accents pronounce it, some don't.
– Deusovi
May 21, 2016 at 2:17

My guess is:

Brown v. Board of Education

Explanation:

Brown v. Board of Education refuted the idea of the "separate, but equal" doctrine. The main statement is that if sets A and B are disjoint, then it's implied A is not equal to B. Another way to describe disjoint sets is separate. So in other words, if A and B are separate, they are NOT equal.

As for the hint (credit goes to pacoverflow for figuring this out):

Brown v. Board of Education was a unanimous 9-0 decision and there are 9 elements in set S (the set of Supreme Court members with concurring opinions).

• Very close, but it's a more specific event. You don't have the right explanation for the hint. May 20, 2016 at 20:34
• Sweet, took another shot at it. :) May 20, 2016 at 20:43
• Nope, still don't have it. May 20, 2016 at 20:44
• Third time's a charm? :) May 20, 2016 at 20:55
• It was a unanimous 9-0 decision. May 20, 2016 at 21:48

Hm. Well, a literal translation yields:

Therefore, all sets that don't intersect are not the same.

I'm not sure how to relate this to a common phrase yet.

• I think it should be all sets that do intersect May 20, 2016 at 21:48
• No, the intersection is the empty set. This means they don't intersect. May 22, 2016 at 2:36