fresh under bathroom sink plumbing diagram or bathroom plumbing diagram rough in bathroom plumbing bathroom plumbing diagram for rough in 92 bathroom sink drain plumbing diagram.
good under bathroom sink plumbing diagram and venting inadequate with kitchen sink plumbing home island sink venting diagram sink venting diagrams 57 bathroom sink plumbing diagram diy.
luxury under bathroom sink plumbing diagram for medium size of sink piping bathroom sink drain assembly diagram for double sink 92 double vanity sink drain plumbing diagram.
luxury under bathroom sink plumbing diagram and fresh under bathroom sink plumbing diagram opinion from plumbing 31 typical bathroom sink plumbing diagram.
best of under bathroom sink plumbing diagram for medium size of sink faucet under bathroom sink plumbing diagram lovely bathroom sink drain 64 bathroom sink plumbing diagram.
good under bathroom sink plumbing diagram or sink pipe diagram large size of sink drain fittings under bathroom sink plumbing diagram lovely pipe 68 dual bathroom sink plumbing diagram.
best of under bathroom sink plumbing diagram or bathroom sink diagram kitchen sink rough in kitchen sink plumbing rough in diagram bathroom piping diagram 22 bathroom sink plumbing rough in diagram.
luxury under bathroom sink plumbing diagram for bathroom plumbing diagram trending bathroom sink 42 bathroom sink plumbing diagram diy.
elegant under bathroom sink plumbing diagram for kitchen sink drain assembly diagram lovely bathroom sink drain assembly diagram 27 typical bathroom sink plumbing diagram.
beautiful under bathroom sink plumbing diagram and bathroom sink plumbing installing the vessel sink drain pipes typical bathroom sink plumbing diagram 37 bathroom double sink plumbing diagram.
new under bathroom sink plumbing diagram or bathroom plumbing rough in diagram bathroom plumbing diagram for rough in bathroom sink plumbing rough in 14 bathroom sink plumbing diagram diy.
inspirational under bathroom sink plumbing diagram and sink rough in bathroom sink marvelous bathroom plumbing diagram for rough in intended for kitchen sink 55 bathroom sink plumbing diagram.
awesome under bathroom sink plumbing diagram and kitchen sink plumbing diagrams recommendations bathroom sink plumbing 75 double bathroom sink plumbing diagram.
idea under bathroom sink plumbing diagram and medium size of kitchen sink drain pipe under bathroom sink plumbing diagram awesome 43 bathroom sink plumbing diagram diy.
The structure of this humble diagram was formally developed by the mathematician John Venn, but its roots go back as far as the 13th Century, and includes many stages of evolution dictated by a number of noted logicians and philosophers. The earliest indications of similar diagram theory came from the writer Ramon Llull, whos initial work would later inspire the German polymath Leibnez. Leibnez was exploring early ideas regarding computational sciences and diagrammatic reasoning, using a style of diagram that would eventually be formalized by another famous mathematician. This was Leonhard Euler, the creator of the Euler diagram.
Usage for Venn diagrams has evolved somewhat since their inception. Both Euler and Venn diagrams were used to logically and visually frame a philosophical concept, taking phrases such as some of x is y, all of y is z and condensing that information into a diagram that can be summarized at a glance. They are used in, and indeed were formed as an extension of, set theory - a branch of mathematical logic that can describe objects relations through algebraic equation. Now the Venn diagram is so ubiquitous and well ingrained a concept that you can see its use far outside mathematical confines. The form is so recognizable that it can shown through mediums such as advertising or news broadcast and the meaning will immediately be understood. They are used extensively in teaching environments - their generic functionality can apply to any subject and focus on my facet of it. Whether creating a business presentation, collating marketing data, or just visualizing a strategic concept, the Venn diagram is a quick, functional, and effective way of exploring logical relationships within a context.
A Venn diagram, sometimes referred to as a set diagram, is a diagramming style used to show all the possible logical relations between a finite amount of sets. In mathematical terms, a set is a collection of distinct objects gathered together into a group, which can then itself be termed as a single object. Venn diagrams represent these objects on a page as circles or ellipses, and their placement in relation to each other describes the relationships between them. Commonly a Venn diagram will compare two sets with each other. In such a case, two circles will be used to represent the two sets, and they are placed on the page in such a way as that there is an overlap between them. This overlap, known as the intersection, represents the connection between sets - if for example the sets are mammals and sea life, then the intersection will be marine mammals, e.g. dolphins or whales. Each set is taken to contain every instance possible of its class; everything outside the union of sets (union is the term for the combined scope of all sets and intersections) is implicitly not any of those things - not a mammal, does not live underwater, etc.
Euler diagrams are similar to Venn diagrams, in that both compare distinct sets using logical connections. Where they differ is that a Venn diagram is bound to show every possible intersection between sets, whether objects fall into that class or not; a Euler diagram only shows actually possible intersections within the given context. Sets can exist entirely within another, termed as a subset, or as a separate circle on the page without any connections - this is known as a disjoint. Furthering the example outlined previously, if a new set was introduced - birds - this would be shown as a circle entirely within the confines of the mammals set (but not overlapping sea life). A fourth set of trees would be a disjoint - a circle without any connections or intersections.
Logician John Venn developed the Venn diagram in complement to Eulers concept. His diagram rules were more rigid than Eulers - each set must show its connection with all other sets within the union, even if no objects fall into this category. This is why Venn diagrams often only contain 2 or 3 sets, any more and the diagram can lose its symmetry and become overly complex. Venn made allowances for this by trading circles for ellipses and arcs, ensuring all connections are accounted for whilst maintaining the aesthetic of the diagram.
Other Collections of Under Bathroom Sink Plumbing Diagram