Question 1 (a) Given E1 = {a,b}, and 22 {a,b}, and E2 = {1, 2, 3} What is the cardinality of ? List all the strings of 21 o 22. List all the strings of 22 o 21. (b) Heapify the following tree, make every step clear. (Min heap) [1] [2] [2] [6] 31 25 19 11 (21 33 28 2 37 (C) Give two strings that can be and two that cannot be generated from (b+a)*6* U (ab+)* U (ab+)*a, if I = {a,b}. Describe the language of this regular expression. [6] (d) What is the minimum number of cards one must pick out of a standard deck of cards to guarantee at least 5 cards are from the same suit? [3] (e) Use mathematical induction to prove that for all natural numbers n > 0, 4"