As far as the closed socials, there might be mixers or closed date parties where everyone in the fraternity will be "paired" with a girl from the sorority you're mixing with - either from a roster or through a game like nuts & bolts. This DOESN'T mean you have to do anything other than talk to her and be polite. Not only that - the girl might not be keen on you or have a boyfriend herself, so that would be a moot point now, wouldn't it?
I agree w/ TrevorG - if she doesn't trust you to hang out with other girls then you have other problems in your relationship. Not only that, if she just assumes sorority women are going to hook up with you at mixers, then she's either got an offensively low opinion of sorority women or thinks you're a cross between Casanova and Adonis.
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