Logical Reasoning

PT127 · S1 · Q17 Curator: Our museum displays only

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Curator: Our museum displays only twentieth-century works, which are either on loan from private collectors or in the museum’s permanent collection.

Statements

conditional (only)

Museum → 20th century work displays it

Museum → On loan from private collector displays it or in museum's perm collection

conditional (all)

Museum's → Prints available in perm collection museum store

quantifier (some)

Some ~Museum's prints available in Perm Collection museum store

Hopper's Nighthawks: not part of museum's permanent collection, but a print of it is sold in the museum store.

Evaluate

We have three-ish conditional ideas, followed by some specific facts, so we have a couple jobs:

1. Do any of these conditionals chain together? 2. Can we apply any of these conditional rules (or their contrapositives) to the specific facts?

We seem to have a bit of a chain, because "museum's permanent collection" is an overlapping idea in the 1st and 2nd sentence.

We know there are some 20th century works on display that are from the museum's permanent collection and thus whose prints can be purchased in the museum store.

Can we infer anything about Nighthawks? The fact that it's not in the permanent connection doesn't really tell us anything. We don't have any rule triggered by "not in permanent connection". And the fact that its print is available in the museum store tells us nothing, because that's just the right side of one of our conditional rules.

Goal

It doesn't look like we can infer anything additional about Nighthawks. Maybe the correct answer will test the connection between the 1st and 2nd sentence, made possible by the overlap of "in the museum's permanent collection".

But ultimately we're just looking for the most provable answer we can find.

17.

If the curator's statements are true, which one of the following must be true?

  1. Every print in the museum

    Too Strong: every

    We don't have any conditional rules that start with "if print is available in museum store". We only have that idea as an outcome. in permanent collection → available in museum store It's possible that some print in the museum store is from the store owner's 10 year old daughter, which is neither a work on loan to the museum or a work that's part of the museum's permanent collection.

    3% picked this

  2. Every print that is sold

    Too Strong: every

    We don't have any conditional rules that start with "if print is sold in museum store". We only have that idea as an outcome. in permanent collection → sold in museum store It's possible that some print in the museum store is from the store owner's 10 year old daughter, which would mean that some prints sold in the store are from 21st century works.

    7% picked this

  3. Correct

    There are prints in the

    Why this is right

    This answer is a quite a mouthful, but it is ultimately just combining the 1st and 2nd sentences. The word "every" shows us the trigger idea: Displayed in museum and → ~on loan from collector Let's pause there and ask ourselves if we would know anything. If it's displayed in the museum, then we know it's a 20th century work that's either on loan from a private collector or in the museum's permanent collection. So if it's "on display, but not on loan", then it would have to be a 20th century work that is in the museum's permanent collection. The 2nd sentence says that everything in the permanent collection is available as a print in the museum store. So, yes, this answer is saying something true. If it's "on display, but not on loan", then it's from the permanent collection, and all of those have prints available in the museum store. We could try to represent this formally, but it would probably be much harder and less likely than just going from the answer choice's trigger and seeing where it takes us. Whenever we have a conditional like A → B or C then you could choose to re-write that as A and ~B → C A and ~C → B So if we re-wrote our original conditional on display → on loan or perm collection in this form, on display and ~on loan → perm collection then we could chain this together with the 2nd sentence: on display museum's prints available and → permanent → in the museum ~on loan collection store

    Skill tested: Must be True · how this choice captures the argument's function is the move to repeat next time.

    61% picked this

  4. Hopper’s Nighthawks is both a

    Unsupported

    We weren't able to derive any additional facts about Nighthawks because the two things we know about it "not part of permanent collection" and "available in museum store" don't trigger any other knowledge.

    22% picked this

  5. Hopper’s Nighthawks is not displayed

    Unsupported

    We weren't able to derive any additional facts about Nighthawks because the two things we know about it "not part of permanent collection" and "available in museum store" don't trigger any other knowledge.

    7% picked this

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