# Math Help - Help me to make equation of three variables

1. ## Help me to make equation of three variables

I would like to make equation with three (x,y,z) variables to calculate the third variable from two. There is a direct relationship of third variables with other two. For example
Z= aX + bY. i want z should lie between 0 and 1. x and y both are liying between 0 and 1. One method is Pythagoras theorem or distance formula. Can any one help me to form the equation with any other formula? I am in dark kindly help me.

2. ## Making equation for third variable

Originally Posted by satwindercse
I would like to make equation with three (x,y,z) variables to calculate the third variable from two. There is a direct relationship of third variables with other two. For example
Z= aX + bY. i want z should lie between 0 and 1. x and y both are liying between 0 and 1. One method is Pythagoras theorem or distance formula. Can any one help me to form the equation with any other formula? I am in dark kindly help me.
One simple formula that might be used is: z = x + y - x y = x + (1 - x) y

If 0 < x < 1 and 0 < y < 1
then (1 - x) y < (1 - x)
amd
x + (1 - x) y < x + (1 - x)
x + (1 - x) y < 1

3. Thanks for ur help.
Can u please tell me the name of the equation known to be? why we subtract the xy from equation.
Other thing is 0 and 1 both are included in x and y. z value is also between 0 and 1 and both 0 and 1 are included in the z in optimal condition?
Can u please help me to project this equation graphically or geometrically?

4. ## Help me to make equation of three variables

Thanks for ur help.
Can u please tell me the name of this equation? why we subtract the xy from equation.
Z value is lie between 0 and 1 and both 0 and 1 are included in the Z in optimal condition only? Another thing i want is Z sholud be 0 when x and y both are 0 and Z should be 1 when x and y both are 1 not other than that.
Can u please help me to project or prove this equation graphically or geometrically?

5. Originally Posted by satwindercse
Thanks for ur help.
Can u please tell me the name of this equation? why we subtract the xy from equation.
Z value is lie between 0 and 1 and both 0 and 1 are included in the Z in optimal condition only? Another thing i want is Z sholud be 0 when x and y both are 0 and Z should be 1 when x and y both are 1 not other than that.
Can u please help me to project or prove this equation graphically or geometrically?
First, equations don't generally have names.

The "xy" was subtracted specifically so that z would be 1 when x and y are both 1: Just x+ y alone would be equal to 2 when x= y= 1 but 1+ 1- (1)(1)= 1.

I don't know what you mean by "optimal condition". There was no mention of "optimal" in your original post.

The formula Kermit1941 gave does exactly what you ask: it is 0 when x and y are 0, 1 when x and y are 1 and only at those points.

I don't know what you mean by "prove" an equation. What do you want to prove about it? -If you mean "prove it is 0 only if x= y= 0", graph y= x/(1- x). If you mean "prove it is 1 only if x= y= 1", graph y= (1-x)/(1- x). If you mean "prove that the equation MUST be this", you can't. There are an infinite number of equations satisfying those conditions Kermit1941 gave you the simplest.

6. Originally Posted by satwindercse
Thanks for ur help.
Can u please tell me the name of the equation known to be? why we subtract the xy from equation.
Other thing is 0 and 1 both are included in x and y. z value is also between 0 and 1 and both 0 and 1 are included in the z in optimal condition?
Can u please help me to project this equation graphically or geometrically?
Name of equation: probability that either event A or event B will happen
if probability of event A is x, and probability of event B is y.

The equation remains valid for 0 and 1 values of x and y.

z = x + y - x y

If x is 1, then regardless of the value of y, z is equal to 1.
If x is 0, then regardless of the value of y, z is equal to y.

The subtracting of x y is to insure that
z will be in the range (0 to 1) provided both x and y are in that range.

When both x and y are equal to 1,
z = 1 + 1 - 1 * 1.

Without the subtraction of x y, z would have been 2.

Another way to look at the reason for subtracting x y is this:

x is a measure of something that I give the name of A.
y is a measure of something that I give the name of B.

I want z to be the measure of everything that is in
either A or B.

It is not enough to simply add x and y because
there may be things that are in both A and B.

x y is the measure of those things in both A and B.

So

z = x + y - x y
z = measure of A + measure of B - measure of things in both A and B.

Thus z is the measure of everything that is in A or B. And we count those
things that are in both A and B only once,
instead of twice, by subtracting xy.

Kermit Rose

7. ## Help me to make equation of three variables

This equation works satisfactorily for me for all the condition except the following:
when x=1 and y=between 0 and 1 or vice versa.

For Example
when x=1 and y=0.2
then z=1+.2-.2=1

but this is not as per my requirement. I want that z=0 or z=1 should come only when x=y=0 and x=y=1 respectively. Otherwise some value should come.

For me optimal condition are when x=y=1 i.e. (1,1) at this point i want z=1.

Can we do some thing by normalizing this equation?
One of u have talk about some other equation can u please suggest me those?

8. How about $z=\frac{x+y}{2}$?
when x=0=y, z=0
when x=1=y, z=1
and when 0<x<1 and 0<y<1 then 0<z<1.