The discovery of an algorithm often begins with a sudden insight into the problem. Sometimes (unfortunately), an idea that. seems very intuitive at first glance, turns out not to be correct on further thought. Figuring out that something is not correct by finding counterexamples is a uscful skill. Among other things, it decpens your understanding of the problem. Find counterexamples for the following propositions: 1. Proposition: a+b>min(a,b) 2. Proposition: the shortest, routc in a road network between two points is oue with the fewest turns. 3. Proposition: being up by a queen in a game of chess guarantees a win