Alright, here's a brain teaser. An ORIGINAL brain teaser that I'm making up right now!

I'm staring at a bag of mixed pretzels and chips
...

If all pretzels are bread
and some chips are bread
and all bread goes well with peanut butter
and some pretzels go well with mustard
and all chips go well with hummus
MUST it therefore follow that:
some bread goes well with mustard
some bread goes well with hummus
all chips go well with peanut butter
all pretzels go well with peanut butter?