1. Consider the set X = {21-1 : nen). (a) List the elements of X that are less than 100. (b) Give an inductive definition of the set X. (Hint: How can you get from one element of X to the next larger element?) [6 marks) 2. Consider the set X C N defined inductively as follows. Basis Clause: 2 X and 5 E X. Inductive Clause: If neX and ke X and nk then nuk eX Extremal Clause: Nothing is in X unless its membership can be established from the above. (a) Give three elements of N which are elements of X, explaining for each one why it is an element. (b) Give three elements of N which are not elements of X, explaining for each one why it is not an element. (C) Give a complete description of the set X using set building notation. [6 marks)