Do b, c, d

Do d, f, j

Do a, b, e, f

In the following question, the domain of discourse is a set of students at a university. Define the following predicates E(x): x is enrolled in the class T(x) x took the test Translate the following English statements into a logical expression with the same meaning. (a) Someone who is enrolled in the class took the test. Solution A 3x (Efx) A T) All students enrolled in the class took the teste MAMA MAMMA Everyone who took the test is enrolled in the class, At least one student who is enrolled in the class did not take the test. seeds In the following question, the domain of discourse is a set of employees who work at a company. Ingrid is one of the employees at the company. Define the following predicates S(x): x was sick yesterday W(x):x went to work yesterday Vxx was on vacation yesterday Translate the following English statements into a logical expression with the same meaning. At least one person was sick yesterday. (b) Everyone was well and went to work yesterday Solution - (-S(x) A W(x)) (e) Everyone who was sick yesterday did not go to work. Solution wx (S(X) --W()) Yesterday someone was sick and went to work Everyone who did not go to work yesterday was sick Everyone who missed work was sick or on vacation (or both). Someone who missed work was neither sick ner on vacation Each person missed work only if they were sick or on vacation (or both). Ingrid was sick yesterday but she went to work anyway Someone other than Ingrid was sick yesterday. (Note for this question, you will need the expression (x Ingrid). W Everyone besides ingrid was sick yesterday. (Note that the statement does not indicate whether or not ingrid herself was siek yesterday. Also, for this question, you will need the expression (x + Ingrid). A student Club holds a meeting. The predicate MIX) denotes whether person x came to the meeting on time. The predicate Oix) refers to whether person is an officer of the club. The predicate Dix) indicates whether person x has paid his or her club dues. The domain is the set of all members of the club. The names of the members and their truth values for each of the predicates is given in the following table. Indicate whether each expression is true or false. If a universal statement is not true give a counterexample, Iran existential statement is true, give an example Name M) O D (X) Donald web Carly F wx-(0(X) - Dx) vx(x+Jeb) ---OX) Dix) (0) wx (-01x) Solution ) ax(M(%) ADEX) ex (MX) v O(x) V DIX) (g) M eb) AD(Hillary) Solution D(Berniej Or Bernie) - ax (O) -- MIX) 3x (MX) OTX) A U{x}