Hello, I need help with the entire question from a) to f). Thank you!

(a) Given 1 = {a,b}, and X2 = {1,2,3} What is the cardinality of ? List all the strings of 0. List all the strings of go. (b) Heapify the following tree, make every step clear. (Min heap) [1] [2] [2] [6] 31 25 19 11 21 33 28 37 [6] (c) Give two strings that can be and two that cannot be generated from (6+a)*** U (ab+)* U (abt)*, if I = {a,b}. Describe the language of this regular expression. (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? (e) Use mathematical induction to prove that for all natural numbers n > 0), 4" 0), 4"