Consider a collision in which particle A (with mass mA and proper velocity ηA) hits particle B (mass mB, proper velocity ηB), producing particle C(mC, ηC) and particle D(mD, ηD). Suppose that (relativistic) energy and momentum are conserved in system S (i.e., pAμ+pBμ=pCμ+pDμ). Using the Lorentz transformations (3.7), show that (relativistic) energy and momentum are *also* conserved in S′. (Do *not* assume that mass is conserved—in general, it is not: mA+mB=mC+mD.)