logic question inferences Here are two inferences A and B, one of which is valid, but the other not valid.
Inference A

  
*
  
*Every human is mortal.
  
*Socrates is human.
  
*Therefore Socrates is mortal.
  

Inference B

  
*
  
*Every hero likes women.
  
*Taro likes women.
  
*Therefore Taro is a hero.
  

Which one is correct, and in what sense it is correct ? 
Can somebody give the hints to solve it ?
 A: Draw a circle. Draw another circle, inside the first. Draw a point inside one of the circles and see if being inside one the circles implies being inside the other.
The difference is like between necessary and sufficient conditions. Being a human is sufficient to be mortal. Being mortal is necessary but not sufficient to be human. Similarly, being a lover is necessary for being a hero but not sufficient. 
In probability, this fallacy is know as Confusion of inverse
A: Hint: Is everyone who likes women necessarily a hero?
A: Hint
Inference B
$\varphi(x)$ mean $x$ likes women
$Hero(p)$ means $p$ is a hero

1) $\forall p:Hero(p)\rightarrow \varphi(p)$
2) $\varphi(taro)$
3) $\varphi(taro)\rightarrow Hero(taro)$

So the second inference is 
$(P\rightarrow Q)\rightarrow (Q\rightarrow P) $
Is this always true?
Inference A
But when we talk about socrate we have a different thing:
$\varphi(x)$ mean $x$ is mortal
$Human(p)$ means $p$ is a human

1) $\forall p:Human(p)\rightarrow \varphi(x)$
2) $Human(socrate)$
3) $Human(socrate)\rightarrow \varphi(socrate)$

that is very different.
