# For any two numbers we define an operation $ yielding another number, X $ Y such that following condition holds: X $ X = 0 for all X , X $ (Y $ Z) = X $ Y + Z Find the Value of 2012 $ 0 + 2012 $ 1912 ?

For any two numbers we define an operation $ yielding another number, X $ Y such that following condition holds: " X $ X = 0 for all X " X $ (Y $ Z) = X $ Y + Z Find the Value of 2012 $ 0 + 2012 $ 1912 ?

A. 2112

B. 100

C. 5936

D. Cannot be determined

### **Answer : ** A. 2112

## Explanation:

Here $ represent the – operator so X - X = 0

First condition x $ (y $ z) = x - (y - z) = x - y + z.

It can be written as x $ y + z

2012 - 0 + 2012 - 1912 = 2112