Just Looking

Logic Level 2

Fran is looking at Andre, who is looking at Gregor.
Fran is married and Gregor is not.
Is a married person looking at a person who is not married?

Yes No Cannot be determined

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Mark C by Mark C , 58, USA

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3 solutions

Mark C
Mar 30, 2016

Disjunctive syllogism is the following kind of reasoning:

  • Either this or that.
  • If this, then so-and-so.
  • If that, then so-and-so.
  • Therefore, so-and-so.

In this case:

  • Either Andre is married or he isn't. Let's consider both possibilities:
  • If he's married, then someone (Andre) who is married is looking at an unmarried person (Gregor).
  • If he's not married, then someone (Fran) who is married is looking at an unmarried person (Andre).
  • Therefore, whether Andre is married or not, someone who is married is looking at an unmarried person.
23 Helpful 0 Interesting 0 Brilliant 0 Confused

However the question does not state if andre is alive

David Kushner - 5 years, 2 months ago

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It doesn't state if Andre (or any of them) is a person either.

Michael Richmond - 5 years, 2 months ago

wow this is a nice problem

Ashley Shim - 5 years, 2 months ago

I can't understand!

Rashid Ansari - 5 years, 2 months ago

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Mark is splitting up the situation into all possible cases. Since it's not stated whether Andre is married or not, he could be either. We can all agree that Andre is either married or not married; there is no in-between or other option. Therefore, if we can prove that someone married from the group (not just Andre) is looking at an unmarried person for both possible cases (Andre is either married or not), then there has to be someone married looking at someone not married. If Andre's not married, Fran (married) is looking at someone not married (Andre). If he is married, he's looking at someone not married (Gregor). Therefore, for all possible cases, someone married is looking at someone not married.

The picture may have also rose some confusion. Here, looking does not imply looking for a partner, but simply looking, and nothing else. You could replace "looking" with "waving his/her hand" without any change to the logic.

Hopefully this clears up any confusion.

Chad Horton - 5 years, 2 months ago

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Thanks, Chad. I've tried to make my solution clearer too.

Mark C - 5 years, 2 months ago

How is this disjunctive syllogism? I get that the problem is of P or Q, but where is (not P) here?

Prathik M - 5 years, 2 months ago

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Either: (Andre is married) or Not (Andre is married). If (Andre is married) then (A married person is looking at a person who is not married). If Not(Andre is married) then (A married person is looking at a person who is not married). Therefore, (A married person is looking at a person who is not married).

But disjunctive syllogism doesn't have to start with a premise of P-or-Not-P. It's fine for it to be a premise of P or Q for any Q. For instance (just an example; the statements may be true or false):

Either Clinton will be the next President or Sanders will be the next President.

lf Clinton is the next President, a Democrat will be the next President.

If Sanders is the next President, a Democrat will be the next President.

Therefore, a Democrat will be the next President.

Mark C - 5 years, 2 months ago
Feathery Studio
Apr 1, 2016

Simply put, there are only two possible combinations. Let M M denote a married person and U U denote an unmarried person. Going on the assumption that a person must be married or unmarried, and not both, there are two possible combinations:

M M M M U U

M M U U U U

If Andre is married, then he will be looking at the unmarried Gregor, therefore fulfilling the condition.

If Andre is unmarried, then he will be looked at by the married Fran, therefore fulfilling the condition.

∴ A married person is looking at an unmarried person.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Amr Abdelnoor
Apr 2, 2016

Fran --> Andre --> Gregor

Married --> Married or Unmarried --> Unmarried

therefore either:

Married --> Married --> Unmarried

or

Married --> Unmarried --> Unmarried

Fran = Married; Gregor = Unmarried; Andre = Can either be Married or Unmarried; - In case Andre is Married, he would be looking at Gregor(Unmarried). so a married person would be looking at an unmarried person - In case Andre is unMarried, Fran (Married) would be looking at him. so again a married person would be looking at an unmarried person. so in all cases, a married person is looking at a person who is not married.

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