Construct garbled circuits

Cryptographic protocols, Autumn 2008, 2nd home exercise

Consider the two-party functionality min(x,y), where the first party inputs x, the second party inputs y and both learn the minimum of those two. Let the two parties use Yao's “garbled circuits” protocol to securely evaluate that functionality (first party garbles, second party evaluates). Construct a circuit C for the functionality min (assume that both inputs, as well as the output are two bits long) and draw the garbled circuit. Also draw the simulated circuits for the following two cases: Show that the simulated circuits are indistinguishable from the actual one.