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I have seen lot of questions of below type predictions. I can't figure out the answer. Is there any common method to solve this ?

Please consider the following example

Statements:-  All cats are dogs. All dogs are cows. Some dogs are pigs. Some chicken are dogs.  Q: Say true or false  A. Some chicken are pigs. B. All pigs are cats. C. Some cows are chicken. 

What is the answer and please explain how you solved this ?

2 Answers 2

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These are are called syllogism, there are various techniques that one could use while solving them the Wikipedia page has a decent discussion.

For your particular problem the answers I got are:

  • A. Some chicken are pigs. (False)
  • B. All pigs are cats. (False)
  • C. Some cows are chicken. (True)
  • 0
    [Modal logic](http://en.wikipedia.org/wiki/Modal_logic) addresses this distinction.2012-01-24
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Let $C$ be the set of all cats; $D$ the set of all dogs; $P$ the set of all pigs; $H$ the set of all chickens (for "hens"); $W$ the set of all cows.

Statement 1 says that $C\subseteq D$.

Statement 2 says that $D\subseteq W$.

Statement 3 says that $C\cap P\neq\varnothing$.

Statement 4 says that $D\cap H\neq\varnothing$.

Statement A says $H\cap P\neq\varnothing$. This cannot be deduced from Statements 1-4; for example, say $C=\{a,b\}$, $D=\{a,b,c\}$, $W=\{a,b,c,d\}$, $P=\{b,q\}$, $H=\{c\}$. Then Statements 1-4 are true, but $H\cap P=\varnothing$.

Statement B says that $P\subseteq C$; again, the example above shows that this cannot be deduced from Statements 1-4 alone.

Statement C says that $W\cap H\neq\varnothing$. This is true: we know there exists some $x\in D\cap H$ (by statement 4), and that $D\subseteq W$ (by statement 2); hence $x\in W$. Since $x\in H$, we obtain $x\in W\cap H$, which is therefore nonempty.

So the syllogisms

Statement 1 Statement 2 Statement 3 Statement 4 ----------- Statement X 

are invalid if X is A or B, and is valid when X is C.