Question

Suppose the domain of the propositional function P ( x, y ) consists of pairs x...

  1. Suppose the domain of the propositional function P ( x, y ) consists of pairs x and y, where x is a, b, c, or d and y is e, f, or g. Write out the following propositions using disjunctions, conjunctions, and negations.
    1. ∃x P ( x, g )

    3. ∀y P ( b, y )

    5. ∃y ¬ P ( a, y )

    7. ∀x ¬ P ( x, e )

    9. ∃x ¬ P ( x, f )
  2. Translate the following statements into idiomatic English where C ( x, y ) means that student x is enrolled in class y, where the domain of x consists of all students in this course (which includes Jane) and the domain of y consists of all classes being offered at your school.
    1. C ( Jane, CMPSC 121 )

    3. ∃x C ( x, IST 242 )

    5. ∀x ( C ( x, CMPSC 101 ) ∧ C ( x, IST 250 ) )

    7. ∀x∀y∃z (( x ≠ y ) ∧ C ( x, z ) ∧ C ( y, z ) )

    9. ∃x∃y∀z (( x ≠ y ) ∧ ( C ( x, z) ↔ C ( y, z ) ) )
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