In this problem, we'll construct two propositions in terms of the variables x, y, z and...

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In this problem, we'll construct two propositions in terms of the variables x, y, z and then use these propositions to build a circuit that computes a binary function M(x, y, z). (a) Give a propositional logic formula containing only the variables y and z which evaluates to ¬y when z is false and evaluates to true when z is true. [2 points] (b) Give a propositional logic formula containing only the variables z and a which evaluates to a when z is true and evaluates to true when z is false. [2 points] (c) Now consider the binary function M(x, y, z) which is defined as: M(x, y, 1) :=x M(x, y,0) := y Draw a circuit that takes x, y, z as input, uses only AND, OR, and NOT gates, and outputs M(x, y, z). Your gates should not take more than two inputs. Your answer for this part must combine your answers from (a) and (b)!) [6 points] In this problem, we'll construct two propositions in terms of the variables x, y, z and then use these propositions to build a circuit that computes a binary function M(x, y, z). (a) Give a propositional logic formula containing only the variables y and z which evaluates to ¬y when z is false and evaluates to true when z is true. [2 points] (b) Give a propositional logic formula containing only the variables z and a which evaluates to a when z is true and evaluates to true when z is false. [2 points] (c) Now consider the binary function M(x, y, z) which is defined as: M(x, y, 1) :=x M(x, y,0) := y Draw a circuit that takes x, y, z as input, uses only AND, OR, and NOT gates, and outputs M(x, y, z). Your gates should not take more than two inputs. Your answer for this part must combine your answers from (a) and (b)!) [6 points]

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a The propositional logic formula that satisfies the given condition is z t... View the full answer