Problem 1.7 [10 points] Purpose: count strings and explore languages. a. How many strings are in the set { win{a,b,c,d, e, f,g}* ||W=9} b. How many strings are in the set { win{a,b,c,d,e, f,g}* ||w=9, #a(w)=4, #b(w)=2} C. Find the shortest string over alphabet {1} that is not in {e, 1, 12, 13, 15} d. Find the shortest string over alphabet {1} that is not in {e, 1, 12, 13, 1573 [note exponent 3] For parts a and b, try out your formula for lengths smaller than 9 to verify they are correct