M(y): y is a math course Flx): x is a freshman T(xy): student x is taking course y 12.(12 points) Suppose the variable x represents students and y represents courses and Uly): y is an upper-level course B(x): x is a full-time student Alx): x is a part-time student Write the statement using these predicates and any needed quantifiers a) Every student is taking at least one course b) There is a part-time student who is not taking any math course 13. (2 points) Suppose the variable x represents students and the variable y represents course, and Tx, y):x is taking y Write the statement in good English. Do not use variables in your answer P(x,y) : x passed y b) vx3yT (x, y) 14. Using the following propositions t Today is Thursday c- I have a test in CS e-I have a test in Econ Translate the following inference into propositional logic If today is Thursday, then I have a test in CS or a test in Econ. If my Econ professor is sick, then I will not have a test in Econ. Today is Thursday and my Econ professor is sick. s- My econ professor is sick. Therefore, I have a test in CS a) (1 point) Translate the above inference into propositional logic (b) (2 points) Is the inference correct? Justify your response