#25- To get the free dessert, one must order an entree and a

[nicholaspavic]

I thought the Either/Or implied automatically implied "at least one" condition.

So if the first sentence of the question were changed to "To get the free dessert, one must order either an entree or
a salad," would that trigger the special either/or construction that I was trying to use? Whereas the sentence I tried to use it on said "they can" as opposed to "must"? Also since the construction is in the necessary condition?

Hi amagari,

You have that correct. It is the matter of "can" vs "must," so well done. If I understand your second question correctly, the special either/or construction can appear in either the sufficient or necessary. There are no restrictions on that. Thanks for the follow up.

[lemonade42]

Hi, I think I'm getting confused by the conclusion: Anyone who is not eligible for a free soft drink is not eligible for a free dessert.

Is this diagrammed as: FSD ---> FD
Because I was thinking of originally diagramming it using the people who are "not eligible" for each condition.
But I had trouble determining who were not eligible. Is it the same as saying the contrapositives?

For example:
1. FD ---> E + S
and contrapositive is E or S ---> FD
does that mean the people who are not eligible for FD is a person without an E or a person without an S?

Also is this stimulus showing valid or invalid reasoning? I was thinking valid reasoning despite the "middle" of the conditional sequence where FD ---> E+S ---> FSD is kind of weird where it includes E or S...

[Dana D]

Hey lemonade,

The stimulus reasoning is sound. We're basically being given a bunch of criteria here. In order to get a free dessert (FD), I have to order an entree and a salad.

FD entree and salad

If I order either an entree or a salad, I'm going to get a free soft drink (FSD)

Entree
or FSD
Salad

Thinking about the contrapositives of these statements, if I fail to order both an entree and a salad, I'm not getting free dessert. If I fail to order either item, I don't get a free soft drink. The free dessert basically has more requirements to win than the free soft drink - if I don't even do the bare minimum required to get that free drink, there's no way I'm getting a free dessert. The contrapositives of each rule would look like this:

Entree and salad FD

FSD Entree or Salad

Be careful when figuring out the contrapositives for and/or statements.

Hope that helps!