A letter is chosen at random from the English alphabet.
a. (i) Construct two non-empty events C and D that are complementary. List each event as a subset of the sample space and explain why they are complementary.
b. (ii) Construct two non-empty events E and F that are mutually exclusive but not exhaustive. Write the sets explicitly and justify both properties.
c. (iii) Construct three events G,H and K that are exhaustive and pairwise mutually exclusive. List the subsets chosen and explain your reasoning.