Polysyllogisms

Deduction, transitive reasoning, polysyllogisms

Introductory note: bniripthians, vritrans, and so on, are classes of characters in the Massively 'Mongous Online Universal Multiuser Multiversal Game (MMOUMUMVG) World of Warped Crafts.

Test the validity of the argument.
Here are the instructions for this problem: If the stated conclusion can be derived by connecting every premise using transitive reasoning, then the argument is valid. If it is not possible to connect all five premises using transitive reasoning, then we may assume that the argument is invalid.
Click the 'Get a clue' link to see the answer(s).

If you aren't a bniripthian then you aren't a khrafrian.
If you are qrdamian then you aren't a gnladent.
All bniripthians are gnladents.
If you are a vritran then you a qrdamian.
No vritran is a czritrian.
Therefore: All khrafrians are czritrians.

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Solution

Test the validity of the argument. In this problem, we are told to assume that, if it is not possible to form a conclusion that requires every premise, then the argument is invalid.

This argument is: Invalid.
We will show that the argument is invalid by showing that it is not possible to form an inference that uses every premise.

If you aren't a bniripthian then you aren't a khrafrian.
If you are qrdamian then you aren't a gnladent.
All bniripthians are gnladents.
If you are a vritran then you a qrdamian.
No vritran is a czritrian.
Therefore: All khrafrians are czritrians.

First, we will symbolize the premises.

	If you aren't a bniripthian then you aren't a khrafrian.	~B→~K
	If you are qrdamian then you aren't a gnladent.	Q→~G
	All bniripthians are gnladents.	B→G
	If you are a vritran then you a qrdamian.	V→Q
	No vritran is a czritrian.	V→~C

Now, we attempt to piece together a chain or reasoning (a polysyllogism), employing every premise. We may replace any premise with its contrapositive if needed.
The first step in our chain of reasoning will be the premise
K→B
We will then try to build upon that.

K→B
B→G
G→~Q
~Q→~V
We have reached a dead end; the chain of reasoning breaks at this step, because we cannot find another premise whose antecedent matches the consequent of ~Q→~V.
It is not possible to form a valid conclusion using every premise.

Copyright 2013, James Wooland.
All rights reserved.
Not to be distributed for commercial purposes.

Solution