Three million dollars was recently stolen from the City Treasurer's Office, and, from what we know so far, we can con...

Olivia on February 5, 2016

Question

@mehran, can you explain how to diagram or work through the part of the question where it talks about "all blank are blank... Some blank are blank." Thanks!

1 Reply

Mehran on February 5, 2016

@odevitt the conclusion here is, "we can conclude that some members of the mayor's staff are suspects."

The support?

Premise 1: The suspects are all former employees of the City Treasurer's Office.

Do not let the location of "all" here trick you. Think about what this statement is saying, i.e. all suspects are former employees of the City Treasurer's Office.

S âž¡ FECTO
not FECTO âž¡ not S

Premise 2: The mayor's staff includes former employees of that office.

So some of the mayor's staff are former employees of the City Treasurer's Office.

MS-some-FECTO
FECTO-some-MS

The variable in common here is FECTO, i.e. former employees of the City Treasurer's Office.

But FECTO is our NECESSARY condition in our Sufficient & Necessary statement (Premise 1). The existence of the necessary condition does not allow us to conclude anything else, so this would be a flawed argument.

Remember, if all else fails on a question like this, the ARROW MUST POINT AWAY from the some/most statement for you to be able to draw a valid conclusion.

Notice here, the only way to combine these statements is as follows:

S âž¡ FECTO-some-MS

The arrow is pointing TOWARDS the some statement, so this is an invalid argument.

Hope this helps! Please let us know if you have any other questions.