Homework Assignments for COMP 3560 Textbook: An Introduction to Formal Languages and Automata, Peter Linz, Fifth Editiorn 1. Suppose that A-(2,4,6), B-(2,6), C (4,6), and D : {4,6,8). Determine which of these sets are subsets of other sets. 2. Let A(a,(a)) and B = { a, {b), {a,b)), Cs(), and D-I}}, How many elements does each of these sets have? 3. Let A (a,b,c) and B-(1, 1211, find the power set for each of A and B. 4. Let A (a,b,c,d) and B- (vz). Find AxB and BxA. 5. Let A (a,b,c), B fx,y), and C (0,1). Find a) AxBxC b) CxBxA c) AxAXA 7. Let S be the set of bit strings and Z be the set of integers. Determine if f is the function from S to Z if given a string s a) f(s) is the position of a 0 bit in s b) f(s) is the number of 1 bits in s. c) f(s) is the smallest integer i such that the ith bit of S is 1 and f(o) - 0 when S is the empty string 8. Find the domain and range of the following functions. a) b) c) d) The function that assigns to each nonnegative integer its last digit. The function that assigns the next integer to a positive integer The function that assigns to a bit string the number of one bits in the string The function that assigns to a bit string the number of bits in the string. 9. Determine whether each of these functions f: ZxZ->Z is one-to-one, on-to, one-to-one correspondence, respectively. a)f(n)=n-1 b)f(n)=n2+1