Exam_2 - EXAM 2 Unless noted otherwise let L be the P C0...

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EXAM 2 Unless noted otherwise let L be the PC 0 language (with equality) generated by the following: H (unary relation symbol), L (binary relation symbol), and a,b,c (constant symbols). 1. True or False (2pts each) The following refer to the semantics for L . (1) ¬ ( a b ) ∧ ¬ ( b c ) | = ¬ ( a c ) (2) {{{}}} and {{}} have the same number of elements. (3) If φ ∈ L and a a | = φ , then φ is a logical truth. (4) If I = h U, ¯ H, ¯ L, ¯ a, ¯ b, ¯ c i is an interpretation of L such that I | = ¬ ( a b ), then U has at least two elements. (5) If A and B are sets, then A × B = B × A . 1
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2 EXAM 2 2. Evaluate (2pts each) Let I be the interpretation of L that is given as follows: U = { 0 , 1 , 2 , 3 , 4 } ¯ H = { 0 , 1 , 3 } ¯ L = { (1 , 1) , (2 , 2) , (3 , 3) , (0 , 4) , (4 , 1) , (4 , 3) } ¯ a = 3, ¯ b = 4, ¯ c = 1 Evaluate the following with respect to interpretation I : (1) ¬ ( a b ) → ¬ ( L ( a,b ) L ( b,a )) (2) ( H ( a ) L
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Exam_2 - EXAM 2 Unless noted otherwise let L be the P C0...

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