Midterm+Answers - MIDTERM ANSWERS 1.1....

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MIDTERM ANSWERS 1.  1. Every atomic formula of  PL is  a formula of  PL . 2. If  is a formula of  PL so  is    P . 3. If  and  are formulas of  PL , so are ( Q ), (   Q ), (   Q ), and (   Q ). 4. If  is a formula of  PL  that contains at least one occurrence of and no  x -quantifier, then ( x ) and ( x ) are both formulas of  PL . 5. Nothing is a formula of  PL  unless it can be formed by repeated applications of clauses 1 to 4. A sentence of  PL  is a formula of  PL  in which there are no free variables. 2.  a.   ( x)[Fxa   formula and sentence truth-functional ( y)Gay] ∼ ∀ b.   ( y)Gyx formula, not a sentence ‘x’ is a free truth-functional variable ∼ ∀ c. ( x)( y)(  Fxy   formula and sentence quantified   Fyx) ∀ ∀ ∼ d. ( z)Faz   ( x)Fxa formula and sentence truth-functional
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This note was uploaded on 03/18/2011 for the course NPB 102 taught by Professor Hahn during the Spring '09 term at UC Davis.

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Midterm+Answers - MIDTERM ANSWERS 1.1....

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