logic 101 (class 2)

i just posted about logic yesterday, and i saw one logic error in facebook today. (facepalm)

let put it in here,

    man cannot change destiny, but personality can change it. 

it seems OK, right. lets just don't discuss what is "destiny" in here, and i reply the post by asking,

   can man change his personality?

by i asking this question is that, the sentence indicated that "man" and "his personality" are independent. and this is natural to ask that "what defined the personality?" it can be anything but "man", say, weather, horoscope, etc. i just want to clarify that. If man cannot change his personality, then the so call "destiny" is really out of man control. and we are all helpless in front of "destiny", like a chess piece.

my friend replied,

  man definite can change his personality.

thus, we can see, "man can change destiny", which contradicted to the statement. because by associative law, we have

   man definite can change his personality.
   personality can change destiny.
   thus, man can change destiny
   but, man cannot change destiny !
   Contradiction!!


Now, we can understand the contradiction, which can be symbolic into.

    Given B, if A then not B.