In the following question, the domain of discourse is a set ofmale patients in a clinical study. Define the followingpredicates:
P(x): x was given the placebo
D(x): x was given the medication
M(x): x had migraines
Translate each statement into a logical expression. Then negatethe expression by adding a negation operation to the beginning ofthe expression. Apply De Morgan’s law until each negation operationapplies directly to a predicate and then translate the logicalexpression back into English.
Sample question: Some patient was given the placebo and themedication.
∃x (P(x) ∧ D(x))
Negation: ¬∃x (P(x) ∧ D(x))
Applying De Morgan’s law: ∀x (¬P(x) ∨ ¬D(x))
English: Every patient was either not
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