visual representation of subsets that comprise the entire set

January 26, 2017 11:46 AM

How would you visually represent (say, with a venn diagram) two subsets of something that 1) comprise the entire set, but also 2) may have some overlap between the two subsets?

Here's an example. Let's say I have a set of "things my wife has asked for her birthday" which are limited to two options: going out for meals and also receiving gifts. However, at some particular time, the meal is such that it is interpreted as a gift. How could these slightly overlapping subsets be represented within the universal set, which is itself only comprised of those two subsets? Is it possible to make a visual diagram of this?

posted by SpacemanStix to Grab Bag (8 answers total)

Why not a Venn diagram? Do you mean something that better represents that there are no options outside the two circles (point (1) above the fold)? I think that's implied by the strict definition, but not usually interpreted as such.
posted by supercres at 11:52 AM on January 26, 2017

Best answer: Ah, never mind-- see here. You'd need to modify it somehow to show that the "universal" set outside of sets A and B is empty.
posted by supercres at 11:56 AM on January 26, 2017 [1 favorite]

Best answer: I made you it.
posted by chesty_a_arthur at 12:00 PM on January 26, 2017 [2 favorites]

Best answer: Yeah this is literally a Venn diagram. The example supercres posted has a box around it to indicate a "superset", but that's not a necessary feature of a Venn diagram.
posted by brainmouse at 12:03 PM on January 26, 2017

Best answer: (or i guess, the superset is "Things that exist in the world", and the set defined by the Venn diagram is "things wife has asked for for her Birthday." )
posted by brainmouse at 12:04 PM on January 26, 2017

Best answer: In a Venn diagram, each circle represents a part of the entire set, and the overlap shows where they overlap. There is no assumption that other things exist outside the circles, because the circles represent the entirety of the subsets which are being examined. There is no need to show more than the circles and their overlap because anything not included in the circles is assumed outside of the considered sets.
posted by hippybear at 12:20 PM on January 26, 2017 [1 favorite]

Response by poster: Okay, that answers it! I was stumbling over what to do with a universal set, but hippybear (and others) get at the heart of it. My project (and I) thank you for your clear and speedy responses.
posted by SpacemanStix at 12:42 PM on January 26, 2017

Best answer: If I'm understanding you correctly, another analogous example might be something like "contiguous US states" and "coastal US states," where some states are both contiguous and coastal, and the union of the two sets comprise all US states (there are no states that are neither contiguous nor coastal).

An Euler diagram might work for this. You can draw it either with or without the individual elements that make up the sets. If drawing it without the individual states, you would draw the outline of the "US states" set very narrowly surrounding the overlapping "contiguous US states" and "coastal US states" set to indicate that there isn't anything in "US states" that isn't also in at least one of its two constituent groups. (If you are showing all the individual states, it doesn't matter if the "US states" outline is narrowly drawn around the others.)
posted by DevilsAdvocate at 12:45 PM on January 26, 2017