please do these

EXERCISE 165. Converting a quantified expression to an equivalent logical expression PIX) is a predicate and the domain for the variable xis (1:2,3,4). For each of the logical expressions given give an equivalent logical expression that does not use quantifiers (a) wxP(X) Solution A P(1) AP(2) P(3) AP(4) (b) 3XPEX EXERCISE 1.7 8. Determining whether a quantified logical statement is true and translating into English part 2 In the following question the domain is a set of male patients in a clinical study Define the following predicates: P(x) xwas given the placebo D(x) * was given the medication A(x) x had fainting spells Mix) x had migraines Suppose that there are five patients who participated in the study the table below shows the names of the patients and the truth value for each patient and each predicate Name Pix) DIX) AX) MIX) Frodo T F T F Gandalf F T F F Gimli F T T F Aragom F T T Bilbo T T F F For each of the following quantified statements, indicate whether the statement is a proposition if the statement is a proposition give its truth value and translate the expression into English fa) ax (MIX) DX)) (b) 2x Mix) A 3X DX) (C) 3x MX) ADI (d) x (A(X) VMX) (e) vx (MIX) -- ALX)) ( vx ((MX) AX)) ---DX)) (g) EX (DK) A-A(X) A-MXX th) x (DX) -- (AX) V M())