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<p>Say if one is a logical consequence of the other Bach. English example QuestionDraw the NAND gate equivalents for each of the following logic gates. Rule-II doubles the I-count. Rule-III reduces the I-count byRule-IV does not change the I-count. Rule-I does not change the I-count. NOT. AND. OR. NOR Simplify the following circuit using only NAND gates by (a) replacing each logic gate with the correct NAND equivalent circuit and (b) removing any redundant logic gates Propositional Logic: exercisesProve that p ∧ ¬p is unsatisfiableProve that p ∨ ¬p is a tautologyWrite the truth table of the following two formula (p ∧ ¬(q ∨ r)) and (¬p ∨ (q ∨ r)). The answer to the question is no. The key is to focus on the number of Is in a string which we call the I-count. (p!r) ^(q!r) (:p_r) ^(:q _r) (:p^:q) _r:(p_q) _r (p_q)!r The equivalence from the second step to the third step is non-trivial, and it might be best to demon-strate it using truth tables (or Venn diagrams, but that won’t come up until section). We begin with a string whose I-count isand our goal is to obtain a string whose I-count Another way to improve your reasoning ability is to read and study on your own and  Givethenamesofthelogicalrelationsthatholdbetweenthefollowing pairs of corresponding categorical statements Yes. (See example from previous exercise.)A valid argument, the conclusion of which is a necessary false-hood Yes: ‘1+1 =So 1+2 =’An invalid argument, the  Brandon Bennett, Logic Examples and ExercisesTranslating from English into First-Order Logic BatchFormulate the following English sentences as formulae in classical  Propositional Logic: exercisesProve that p ∧ ¬p is unsatisfiableProve that p ∨ ¬p is a tautologyWrite the truth table of the following two formula (p ∧ ¬(q ∨ r)) and (¬p ∨ Givethenamesofthelogicalrelationsthatholdbetweenthefollowing pairs of corresponding categorical statements example that illustrates the logic. Say for each one if it is a tautology, satisfiable or contradiction. Answering the logic and reasoning questions in this book will give you lots of practice.</p></translate>
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