 In these equations logical symbols are used to represent mathematical functions on binary variables: ~X = 1 − X; X v Y = max{X, Y}; X &amp; Y = min{X, Y}. The first two equations simply state the actual values of the exogenous variables ST and BT. The third equation encodes two counterfactuals, one for each possible value of ST. It states that if Suzy had thrown a rock (which in fact she did), her rock would have hit the bottle; and if she hadn’t thrown a rock, it wouldn’t have hit the bottle. The fourth equation encodes four counterfactuals, one for each possible combination of values for BT and ~SH. It states that if Billy had thrown a rock and Suzy’s rock hadn’t hit the bottle, Billy’s rock would have hit the bottle, but it wouldn’t have done so if one or more of these conditions had not been met. The fifth equation also encodes four counterfactuals, one for each possible combination of values for SH and BH. It states that if one or other (or possibly both) of Suzy’s rock or Billy’s rock had hit the bottle, the bottle would have shattered; but if neither rock had hit the bottle, the bottle wouldn’t have shattered.