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Let P(x), Q(x), and R(x) be the statements “x is a
professor,” “x is ignorant,” and “x is vain,” respectively.
Express each of these statements using quantifiers; logical
connectives; and P(x), Q(x), and R(x), where the
domain consists of all people.

  • a) No professors are ignorant.
  • b) All ignorant people are vain.
  • c) No professors are vain.

Can someone explain each of the given Predicates?

1 Answer

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2 votes
a. ∀x(P(x) → ~ Q(X))

b. ∀x(Q(x) → R(X))

c. ∀x(P(x) → ~ R(X))

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