$1.$ Define a set X of strings in the symbols $0$ and $1$ as follows. B$.0$ and $1$ are in X$.$ R$1.$ If x and y are in X$,$ so is xxyy$.$ R$2.$ If x and y are in X$,$ so is xyx$.$ Using the definition, explain why the string $110011100$ X$.$ Build up the string step by step, and justify each step by referencing to the appropriate part of the definition.