Simplify :
`x - y - {x-y - (x+y)-bar(x-y)}`

Answer

To simplify the expression \( x - y - \{ x - y - (x + y) - \overline{(x - y)} \} \), we will follow these steps:

### Step 1: Rewrite the expression
We start with the original expression:
\[ x - y - \{ x - y - (x + y) - \overline{(x - y)} \} \]

### Step 2: Simplify inside the curly braces
First, we simplify the expression inside the curly braces:
\[ x - y - (x + y) - \overline{(x - y)} \]
This can be rewritten as:
\[ x - y - x - y - \overline{(x - y)} \]

### Step 3: Combine like terms
Now, combine the like terms:
\[ (x - x) + (-y - y) - \overline{(x - y)} = 0 - 2y - \overline{(x - y)} = -2y - \overline{(x - y)} \]

### Step 4: Substitute back into the original expression
Now, substitute this back into the original expression:
\[ x - y - (-2y - \overline{(x - y)}) \]
This simplifies to:
\[ x - y + 2y + \overline{(x - y)} \]

### Step 5: Combine the terms
Now, combine the terms:
\[ x + (2y - y) + \overline{(x - y)} = x + y + \overline{(x - y)} \]

### Step 6: Final expression
Thus, the simplified expression is:
\[ x + y + \overline{(x - y)} \]