Give a description representation of a Turing Machine Mg for language B = {w over {0, 1, #)* | w contains an equal number of O's and 1's and w contains exactly 1 '#'). 10# € B, 01#10 E B, 01##01 € Band #001 € B. In this case, your description should be for a single tape TM.

Let C(x. v) be x is enrolled in y, where the domain for x is the set of all students at a certain university and the domain for y is the set of all computer science classes being offered at the university. Match each English statement with its equivalent logical expression. ? v 1. No one is enrolled in both CS222 and CS252. A. -3x(C(x, CS222) ^ C(x, CS252)) B. C(Sarah, CS232) C. Ex(C(x, CS222) v C(x, CS252)) D. Vx3yC(x, y). E. 3yVxC(x, y) F. -Vx(C(x, CS222) A C(x, CS252)) G. VyC(Sarah, y) H. 3XVYC(x, y) 1. 3x(C(x, CS222) A C(x, CS252)) J. ByC(Sarah, y) v 2. Everyone is enrolled in some computer science classes, ? v 3. Sarah is enrolled in some computer science class. ? v 4. Someone is enrolled in all domputer science classes. v 5. Someone is enrolled in both CS222 and CS252. ? v 6. There is one class that is enrolled by all students.

Suppose P(x,y) is some binary predicate defined on a very narrow domain ofdiscourse: just the integers 1, 2, 3, and 4. Based on the following table, P(x,y) is trueor false for each of the 16 pairs of these numbers (x values are rows, y values arecolumns).1 2 3 41 T F F F2 F T T F3 T T T T4 F F F FFor example, P(1, 3) is false, as indicated by the F in the first row, third column.Use the table to decide whether the following statements are true or false.a. ∀x∃Yp(x, y).b. ∀y∃xP(x, y).c. ∃x∀yP(x, y).d. ∃y∀xP(x, y).