How can I implement XOR using basic mathematical operators like +,-,*,/
Update: Actually, I need to track change in two matrix having Boolean values. This can be done using XORing each value with corresponding value in other matrix. But, Lp_Solve library doesn't support XOR operation. Also, it accepts only linear equations.
Answer
(a − b)²
This works because:
(a − b)² = a * (a − b) + b * (b − a)
Since multiplication in ℤ₂ is conjuction (&), and 1 - a is negation (!), the above formula is equivalent to XOR for a, b ∈ {0, 1}:
(a & !b) | (b & !a)
See the comment below by Pascal Cuoq explaining why this cannot be a linear equation.