The red 1 to which we will receive no satisfactory reply...2each contained in some universe U, i.e. U is a set and X CUDY3 each contained in some universe U, i.e. U is a set and X CUY4each contained in some universe U, i.e. U is a set and X CU Ɔ Y and Z CU5there is such a thing: Boolean algebra, see https://en.wikipedia.org/wiki/Boolean,lgebra(I prefer to refer to it as Boolean arithmetic). In lieu of asking what a set is, we should ask what we can do with sets. Forexample, from two sets X and Y can we construct their (Cartesian) product:XxY, and e.g. (the proof of) "the size of the product of two sets is the productof their sizes" (has been requested for extra credit).The union of sets X and Y, denoted XUY, is defined viaXUY:= {u € Uu € X or u € Y}The intersection of sets X and Y³, denoted XnY, is defined viaXNY := {u € U\u € X and u € Y}(2)Prove "intersection distributes over union", i.e. for any three sets X, Y,and Z1,Xn(YUZ) = (XnY)u(Xnz).So, in some "arithmetic of sets", there is a distributive property.This suggests the following (purposefully incomplete) table of analogies:Arithmetic Sets+(1)1(3)Complete the above table of analogies now that we're aware of thisdistributive property of the arithmetic of sets.

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Prove "intersection distributes over union"

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter5: Similar Triangles

Section5.2: Similar Polygons

Problem 11E: a Does the similarity relationship have a reflexive property for triangles and polygons in general?...

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Question

The red

1 to which we will receive no satisfactory reply...
2each contained in some universe U, i.e. U is a set and X CUDY
3 each contained in some universe U, i.e. U is a set and X CUY
4each contained in some universe U, i.e. U is a set and X CU Ɔ Y and Z CU
5there is such a thing: Boolean algebra, see https://en.wikipedia.org/wiki/Boolean,lgebra
(I prefer to refer to it as Boolean arithmetic).

In lieu of asking what a set is, we should ask what we can do with sets. For
example, from two sets X and Y can we construct their (Cartesian) product:
XxY, and e.g. (the proof of) "the size of the product of two sets is the product
of their sizes" (has been requested for extra credit).
The union of sets X and Y, denoted XUY, is defined via
XUY:= {u € Uu € X or u € Y}
The intersection of sets X and Y³, denoted XnY, is defined via
XNY := {u € U\u € X and u € Y}
(2)
Prove "intersection distributes over union", i.e. for any three sets X, Y,
and Z1,
Xn(YUZ) = (XnY)u(Xnz).
So, in some "arithmetic of sets", there is a distributive property.
This suggests the following (purposefully incomplete) table of analogies:
Arithmetic Sets
+
(1)
1
(3)
Complete the above table of analogies now that we're aware of this
distributive property of the arithmetic of sets.

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