Deductive Logic

  Deductive Logic   Problem 1: Translate the following argument into categorical syllogistic form (major premise, minor premise, conclusion), symbolize the argument (using the conventional S, P, M variables), and draw a Venn diagram to test its validity. [8p] All bacon burgers are heart attack—inducing foods because all bacon burgers are high-fat foods, and some heart attack—inducing foods are not high-fat foods. For extra credit (up to 4 points): test the validity of the above argument using one of the other methods covered in class. Problem 2: Consider the following statement All newspapers identical to Washington Post are untrustworthy sources. Assuming that this statement is false, use the Square of Opposition to determine the truth-values of the corresponding categorical statements E, I, and O. [2p each] Problem 3: Using the direct truth-table method, determine the validity of the following argument [8p: 6p for the truth-table, 2p for the answer] B → S / S → ~ R / R → (~ B  ~ S) / ~ S // ~ B Problem 4: Three witnesses to a bank robbery gave the following statements. Witness 1: Lefty did not enter the bank, and if Howard pulled a gun, then Conrad collected the money. Witness 2: If Howard did not pull a gun, then Lefty entered the bank. Witness 3 If Conrad collected the money, then Howard pulled a gun. Using the indirect truth-table method, determine whether the witness statements are accurate (i.e., if they are consistent). [8p] If so, what can be concluded about Howard, Conrad, and Lefty? [extra credit: 3p] The above statements can be expressed in symbolic notation as follows: Witness #1: ~L & (H → C) Witness #2: ~H → L Witness #3: C → H (where L: Lefty entered the bank, H: Howard pulled a gun, and C: Conrad collected the money)