Question

Can someone help in this question?

Answer 1

if we choose the color (bc)
a*bc = bc rule iv
b*bc = bc rule i
c*bc = bc *c rule ii
= bc

Answer 2

Can you explain the question once? I have no idea about the question.

Answer 3

do you understand the rules ?

Answer 4

Sort of, but I guess first I got to understand the question. :/

Answer 5

you have to find a color "x" such that ax=x ; bx=x & cx=x

Answer 6

What does it mean when they say, x and y are among a, b & c?

Answer 7

Does among mean, like a mixture of the colors?

Answer 8

well it also can be one of the colors not only a mixture.. it means x and y are from these colors, one color or a mix of them

Answer 9

So x and y can be any of the subsets of a,b,c ?

Answer 10

And even xy is a subset of a,b,c?

Answer 11

it is better to say a combination instead of subset, but if you mean that yes xy is also a combination of a,b,c

Answer 12

Okay, got it. Now we have to find a combination of a,b,c that follows the rules and gives the same color yeah?

Answer 13

any combination you find follows the rules.. you must use these rules to prove (ax=x ; bx=x , cx=x)

Answer 14

So there you took.

x = bc yeah?

Answer 15

yes

Answer 16

a*bc = bc [by fourth rule]

b*bc = bc [HOW?]

c*bc = bc [HOW?] O.O

Answer 17

b*bc = bbc
bb=b
bbc=bc

Answer 18

c*bc = bc*c = bcc = bc

Answer 19

"b*bc = bbc
bb=b
bbc=bc"

xx = x [from first rule]
but here, x = bc! [how is bb = b?]

Answer 20

they used x to generalize the rules, but you can use them for any color you are using

Answer 21

But here when we are considering x to be bc

Do we not have to go with x = bc everywhere?

if x = bc

then

bc*bc = bc [from first rule]
but
b*b \(\neq\) b [because x = bc already]

I am not really getting it.

Answer 22

but if we read what they say between brackets
"mixing a color with itself results in that color"
they said (a color) which means any color not only x

Answer 23

Oh okay! And do x and y and z also have to be any combination of a,b and c?

Answer 24

yes

Answer 25

Can you stay online for like 15 more minutes or more?
I NEED to submit this by today, I'll just try to do it once on my own now.
Thanks!

Answer 26

okay i'm here if you need any help :)

Answer 27

By the way, how did you select 'bc' directly? Any method? Or a random guess?

Answer 28

i found it logical and tried to prove it, it can be considered as random guess

Answer 29

Your method is 100% right. But I just want to know, if I can also guess like that for my submission.

Answer 30

well we can say
to satisfy ax=x x can be any color
to satisfy bx=x x must contain b
to satisfy cx=x x must contain c
so x must be a combination of b and c

Answer 31

Why must 'x' contain b in bx? O.O

Answer 32

so that the b is eliminated
we must have bb=b so only the b included in x remains

Answer 33

That makes a lot of sense, thanks a lot man, I'll just do this on fresh sheet of paper in some time. :D

Answer 34

glad to help :D