# What's the logical difference between two sentences?

These are from an LSAT:

1. No nonfiction book published by Carriage Book has ever earned a profit. Since Carriage Book earned a profit on every book it published last year, it clearly did not publish a nonfiction book last year.
1. No hotel owned by the Bidmore Group specializes in serving business travelers. Since the Cray Springs Hotel is owned by the Bidmore Group, it clearly does not specialize in serving business travelers.

I noted there is a difference in their time frame, 1. concerns what has happened so far while 2. uses the present tense. But does this matter in terms of their logical implication, like in terms of mathematical logic or else?

• I’m voting to close this question because this is not a homework forum Mar 1, 2021 at 5:08
• Very little, at best and why are you Asking this in Philosophy, rather than Logic or, for instance, pin-dancing? Mar 3, 2021 at 23:10

1. No nonfiction book published by Carriage Book has ever earned a profit. Since Carriage Book earned a profit on every book it published last year, it clearly did not publish a nonfiction book last year.

Y = "book that earned a profit"

Z = "books that Carriage Book published last year"

No X are Y. All Z are Y. Therefore, no X are Z.

1. No hotel owned by the Bidmore Group specializes in serving business travelers. Since the Cray Springs Hotel is owned by the Bidmore Group, it clearly does not specialize in serving business travelers.

X = "hotel owned by the Bidmore group"

Y = "hotel that specializes in serving business travelers"

Z = "Cray Springs hotel"

No X are Y. Z is X. Therefore, Z is not Y.

The difference is whether Z is Y (as in #1) or whether Z is X (as in #2).

• "no X are Y" is actually logically equivalent to "no Y are X" though--in both cases, if you think of a Venn diagram for X and Y, the statement is saying they can have no overlapping region. So the first sentence of the first one is logically equivalent to "no book that earned a profit has ever been a nonfiction book published by Carriage book". So with X="book that earned a profit" and Y="nonfiction book published by Carriage book" you could write it as "No X are Y. All Z are X. Therefore, no Z are Y." Then the difference would just be that this allows for multiple Z's, the second doesn't. Feb 28, 2021 at 7:01
• @Hypnosifl yes, you are right, just a difference in phrasing/order, and that the second is an individual Z. Feb 28, 2021 at 8:29

The two lines of reasoning are both valid, but for different reasons. This answer follows up on causative’s answer, which I think is correct.

In the first example, the second premise should be stated first. The major premise has the predicate of the conclusion (Z in #1 and Y in #2).

With that adjustment, the first example is AEE in the second figure. The second example is EAE in the first figure. Both are valid.