How do i show if this is associative or not?

[gavin123]

Homework Statement

(x*y)=x+2y+4

Homework Equations

The Attempt at a Solution

first i did this but I'm not sure if it is correct
(x*y)*z=x+2y+4*z=x+2y+4+z+1
x*(y*z)=x*y+2z+4=x+y+2z+4+1

 

[Svein]

first i did this but I'm not sure if it is correct

No, it is not correct. Study the definition closely. Remember that x does not stand for "x", but for "any expression to the left of "*". Vice versa for y.

 

[gavin123]

I don't understand what you mean?

 

[SteamKing]

I think Svein means that instead of using the notation (x*y) = x + 2y + 4, you should use something like (x⊗y) = x + 2y + 4.

Using '*' as an operator confuses, as we are used to thinking of '*' as indicating multiplication of the quantities x and y.

By using the special ⊗ symbol as an operator, it becomes less confusing.

For example, if we wrote (6⊗y), that would mean 6 + 2y + 4;
likewise (x⊗6) would mean x + 2*6 + 4;
(g⊗x) = g + 2x + 4

 

[gavin123]

Oh ok then did I write it out correctly

 

[SteamKing]

Oh ok then did I write it out correctly

It's not clear what you mean here.

To take one of the items from the OP:
(x ⊗ y) ⊗ z would mean finding out what (x ⊗ y) was first and then combining that quantity with z.

You could re-write the original expression as

(x ⊗ y) ⊗ z = (x ⊗ y) + 2z + 4 and then expand (x ⊗ y) according to the definition.

 

[SammyS]

Homework Statement

(x*y)=x+2y+4

Homework Equations

The Attempt at a Solution

first i did this but I'm not sure if it is correct
(x*y)*z=x+2y+4*z=x+2y+4+z+1
x*(y*z)=x*y+2z+4=x+y+2z+4+1

I don't see any problem in using the asterisk (*) for the operation defined here. Just be sure not to confuse it with traditional multiplication.

When you write:

(x*y)*z = x+2y+4*z ,​

you really should use parentheses,

(x*y)*z = ( x+2y+4 )*z​

What you write after that is incorrect. It should be equal to ( x+2y+4 ) + 2z + 4 , etc.

 

[symbolipoint]

Not showing all my steps, NOT associative.
The two sides give x+2y+2z+8 and x+2y+4z+12, so these are unequal.

 

[gavin123]

so if (x*y)=x+2y-xy Then
x*(y*z)=x+2(y+2z-yz)-x(y+2z-yz) and
(x*y)*z=(x+2y-xy)+2z-(x+2y-xy)z

 

[SammyS]

so if (x*y)=x+2y-xy Then
x*(y*z)=x+2(y+2z-yz)-x(y+2z-yz) and
(x*y)*z=(x+2y-xy)+2z-(x+2y-xy)z

Yes.

But it's not clear, looking at that, whether those two expressions are equivalent.

 

[gavin123]

they are not the same

 

[SammyS]

they are not the same

i know that, but it's not all that clear from those two expressions.