2. Draw Venn diagrams and shade the areas corresponding to the following sets: (a) (AUB) - (AUD) (b) (AU BUC) U BUC) (b)[(AUB) nC]U (AUC) 3. A customer visiting a certain department store will purchase a suit with a probability of 0.22, a shirt with probability 0.30, and a tie with probability 0.28. The customer with purchase both a suit and a shirt with probability 0.11, both a suit and a tie with probability 0.14, and both a shirt and a tie with probability 0.10. A customer will purchase all three items with probability 0.06. (a) What is the probability that the customer purchases at least one of these items? (b) What is the probability that the customer purchases exactly two of these items? (c) What is the probability that the customer purchases a tie given that he has already purchased a shirt and a suit