Exam 2: The Logic of Compound Statements

Draw the circuit that corresponds to the following Boolean expression: $( P \wedge Q ) \vee ( \sim P \wedge \sim$ Q).(Note for students who have studied some circuit design: Do not simplify the circuit; just draw the one that exactly corresponds to the expression.)

Find a circuit with the following input/output table. P Q R S 1 1 1 0 1 1 0 0 1 0 1 1 1 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 0 0

Which of the following is a negation for "Jim is inside and Jan is at the pool."

Write the following two statements in symbolic form and determine whether they are logically equivalent. Include a truth table and a few words explaining how the truth table supports your answer. If Sam is out of Schlitz, then Sam is out of beer. Sam is not out of beer or Sam is not out of Schlitz.

Determine whether the following argument is valid or invalid. Include a truth table and a few words explaining why the truth table shows validity or invalidity. If Hugo is a physics major or if Hugo is a math major, then he needs to take calculus. Hugo needs to take calculus or Hugo is a math major. Therefore, Hugo is a physics major or Hugo is a math major.

Consider the argument form: p\rightarrow\simq q\rightarrow\simp \therefore p\veeq Use the truth table below to determine whether this form of argument is valid or invalid. Annotate the table (as appropriate) and include a few words explaining how the truth table supports your answer. p q \simp \simq p\rightarrow\simq q\rightarrow\simp p\veeq T T F F F F T T F F T T T T F T T F T T T F F T T T T F