# HW6 - 5 Using algebraic equations prove(Forall x...

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Sheet1 Page 1 CS 2603 Applied Logic for Hardware and Software Homework 6 FAQ Due March, 2:59pm (bring your paper to class, and turn it in there) Late Homework will be not accepted 1. Use natural deduction to prove: (Exists x. f(x)) \/ (Exists x. g(x)) |- Exists x. (f(x) \/ g(x)) 2. Define predicates f and g for which (Forall x. (f(x) \/ g(x))) is true, but ((Forall x. f(x)) \/ (Forall x. g(x 3. Use natural deduction to prove: ((Forall x. (f(x) -> h(x))) /\ (Forall x. (g(x) -> h(x)))) |- (Forall x. ((f( 4. Using algebraic equations, prove: (Exists x. (Forall y. (f(x) /\ g(y)))) = ((Exists x. f(x)) /\ (Forall y. g(
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Unformatted text preview: 5. Using algebraic equations, prove: ((Forall x. f(x)) -> (Exists y. g(y))) = (Exists x. Exists y. (f(x) -> g( 6. Using algebraic equations, prove: ((Forall x. (f(x) -> h(x))) /\ (Forall x. (g(x) -> h(x)))) = (Forall x. ((f 7. Suppose that, given an sequence xs and any value x whose type is the same as the type of the e What To Turn In * A paper with solutions to the required problems (staple multiple sheets together - no paper clips). * No files or Haskell sessions are required....
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