WARNING: This is discussion involves formal logic of the type that is not needed on the GMAT. Formal logic does more to confuse that to help those studying for the GMAT.

Your two statements do not link up at all.

This is why Venn Diagrams are not properly used to PROVE something but instead to disprove something. So I can disprove your conclusion that "some girls are not terrorists" by simply saying that "all girls are terrorists." There is nothing in your statements to disprove this. You say "some" girls are arrogant but "some" allows for "all." As in "some people breathe oxygen" which of course is "all people."

So I can draw a diagram with a really big circle for arrogant, a slightly smaller circle completely inside that for terrorists and then a smaller circle completely inside that one for girls. So you can see that all girls would be terrorists and all terrorists arrogant.

My advice to you is not to worry about this. I have taught the LSAT for many years and never miss a question on formal logic. Yet, I have NEVER used formal logic on the GMAT. I have never drawn a Venn diagram on the GMAT.

This stuff is fun though!