In this question, the domain of discourse is a set of male patients in a clinical study.

Define the following predicates:

P(x): x was given the placebo

D(x): x was given the medication

A(x): x had fainting spells

M(x): x had migraines

Translate the following logical expressions into English:

(a) x ( M ( x ) D ( x ))

(b) x (( M ( x ) A ( x )) D ( x ))

(c) x ( D ( x ) A ( x ) M ( x ))

(d) x ( D ( x ) ( A ( x ) M ( x )))