Let [math]X[/math] and [math]Y[/math] be two random variables defined on the finite sample space [math]\Omega[/math]. Assume that [math]X[/math], [math]Y[/math], [math]X + Y[/math], and [math]X - Y[/math] all have the same distribution. Prove that [math]P(X = Y = 0) = 1[/math].