Criticize the following proof by induction of the proposition, "happy families are all alike." consider a set consisting of one happy family. obvi- ously all its elements are the same. suppose it has been shown that for any set of n happy families, say {}, we have fi f2 ==fn. con- sider a set {f1. n+1} of n+1 happy families. then {f1.) is a set of n happy families, so f1 = f2 = = fn. similarly, {f2, f3, fn+1} is a set of n happy families, so fn+1 = = f2. thus fr+1 = fi also, and the set of n + 1 happy families are all alike. by the principle of induction, we see that for any finite set of happy families, they are all alike. since the set of all happy families is finite, we conclude: happy families are all alike.