Sheet2 - McMaster University Department of Computing and...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
McMaster University Department of Computing and Software Dr. W. Kahl COMP SCI 1FC3 Exercise Sheet 2 COMP SCI 1FC3 — Mathematics for Computing 16 January 2009 Exercise 2.1 — Predicates, formal and English From the textbook section 1.3, do at least exercises 10–14, 25, 28, 30. 38–42 (pp. 47–49). Exercise 2.2 — Predicate Logic Equivalences Using logical equivalences from the text book, prove the following: (a) (∃ x ( P ( x ))) ∨ (∃ x ( Q ( x ))) ≡ ∃ x ( P ( x ) ∨ Q ( x )) Using semantic arguments (and possibly logical equivalences), prove the following (assuming x does not occur free in A , and that the domain of quanti±cation is non-empty): (b) (∀ x ( P ( x ))) ∧ A ≡ ∀ x ( P ( x ) ∧ A ) (c) (∃ x ( P ( x ))) ∧ A ≡ ∃ x ( P ( x ) ∧ A ) (d) x ( A P ( x )) ≡ A → ∀ x ( P ( x )) (e) x ( A P ( x )) ≡ A → ∃ x ( P ( x )) (f) x ( P ( x ) → A ) ≡ (∀ x ( P ( x ))) → A ) (g) x ( P ( x ) → A ) ≡ (∃ x ( P ( x ))) → A
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.
Ask a homework question - tutors are online