In each part of this question, you are asked to give an example of something, and explain why it is an example. You may use all definitions, lemmas, theorems etc. from the lecture notes. (a) A cut A C Q such that A' = (5)R.\f(c) A convergent sequence (an ) such that every an is irrational, but lim,-+ an is a rational number.(d) An infinite, bounded above subset A CQ that is not a cut