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Exercise 3

Avg difficulty 2.5

Translate these statements into English where F(x)F(x) is “xx is fast” and A(x)A(x) is “xx is an athlete”, here the domain is the set of people.

  1. ∀x(A(x)→F(x))\forall x (A(x) \to F(x))
  2. ∀x(F(x)∧A(x))\forall x (F(x) \land A(x))
  3. ∃x(F(x)→A(x))\exists x (F(x) \to A(x))
  4. ∃x(A(x)∧¬F(x))\exists x (A(x) \land \neg F(x))

Hammond, Discrete Math for Shockers, §2.3 Propositional Functions and Quantifiers, Exercise 3

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Adapted from Discrete Math for Shockers © 2021 John Hammond. Licensed under CC BY-SA 4.0. Source: Discrete Math for Shockers. Imported at revision 2538beb.