3. There is a buyer with value v E [0, 1] and a seller with cost ce [0, 1]. A mechanism consists of an allocation q(v, c) E {0, 1} and a transfer t(v, c) 2 0. Payoffs are UB(v, C) = q(v, c)v - t(v, c) Us(v, c) = t(v, c) - q(v, c)c. We impose stronger (IC) and (IR) as below: (ICB)q(v, c)v - t(v, c) 2 q(v', c)v - t(v', c) (ICS)t(v, c) - q(v, c)c 2 t(v, c') - q(v, c)c (IRB) q(v, c)v - t(v, c) 2 0 (IRS)t(v, c) - q(v, c)c 2 0. (a) Show that (IR) imply q(v, c) = t(v, c) = 0 if v