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 ?
On
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
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Statement X
are invalid if X is A or B, and is valid when X is C.
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: