Could you help me with this one too? Let T be a equilateral triangle with each side having length 1. ImagineT in a fixed position in the plane, say with the bottom side on the x-axisand the opposite angle above it. Let S be the set of coloured trianglesobtainable from T by painting each side with one of the colours redand blue. Any combination of colours is allowed, for example all sidescould have the same colour. Note that S has 8 elemnents: for examplethe bottom side being red and all other sides being blue is a differentpainting than the leftmost side being red and all other sides being blue.Define a relation R on S by s1 R s2 if and only if s1 can be rotated sothat the rotated coloured triangle is identical to s2. Prove that R is anequivalence relation and find the equivalence classes. (The elements ofyour sets can be pictures of the coloured triangles.)

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Description: Could you help me with this one too? Let T be a equilateral triangle with each side having length 1. ImagineT in a fixed position in the plane, say with the bottom side on the x-axisand the opposite angle above it. Let S be the set of coloured triang

There are 8 kind of equilateral triangle from two colors red(R) and blue(B). RRR-S1 BBB-S2 RBR-S3…

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Let T be a equilateral triangle with each side having length 1. Imagine T in a fixed position in the plane, say with the bottom side on the x-axis and the opposite angle above it. Let S be the set of coloured triangles obtainable from T by painting each side with one of the colours red and blue. Any combination of colours is allowed, for example all sides could have the same colour. Note that S has 8 elements: for example the bottom side being red and all other sides being blue is a different painting than the leftmost side being red and all other sides being blue. Define a relation R on S by s1 R s2 if and only if si can be rotated so that the rotated coloured triangle is identical to s2. Prove that R is an equivalence relation and find the equivalence classes. (The elements of your sets can be pictures of the coloured triangles.)

Let T be a equilateral triangle with each side having length 1. Imagine T in a fixed position in the plane, say with the bottom side on the x-axis and the opposite angle above it. Let S be the set of coloured triangles obtainable from T by painting each side with one of the colours red and blue. Any combination of colours is allowed, for example all sides could have the same colour. Note that S has 8 elements: for example the bottom side being red and all other sides being blue is a different painting than the leftmost side being red and all other sides being blue. Define a relation R on S by s1 R s2 if and only if si can be rotated so that the rotated coloured triangle is identical to s2. Prove that R is an equivalence relation and find the equivalence classes. (The elements of your sets can be pictures of the coloured triangles.)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Could you help me with this one too?

Let T be a equilateral triangle with each side having length 1. Imagine
T in a fixed position in the plane, say with the bottom side on the x-axis
and the opposite angle above it. Let S be the set of coloured triangles
obtainable from T by painting each side with one of the colours red
and blue. Any combination of colours is allowed, for example all sides
could have the same colour. Note that S has 8 elemnents: for example
the bottom side being red and all other sides being blue is a different
painting than the leftmost side being red and all other sides being blue.
Define a relation R on S by s1 R s2 if and only if s1 can be rotated so
that the rotated coloured triangle is identical to s2. Prove that R is an
equivalence relation and find the equivalence classes. (The elements of
your sets can be pictures of the coloured triangles.)

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