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 N defined inductively as follows Basis Clause: 2 EX and 5 EX Inductive Clause: If ne X and keX and nuk then nuk e X. Extremal Clause: Nothing is in X unless its membership can be established from the above. (a) Give three clements 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 clement. (c) Give a complete description of the set X using set building notation. [6 marks