Deductive Logic

show your work.
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)