No - they are not legal.
The / is not a separator -- it means that those words are interchangeable. Look at the second part of the sentence -- "school logo/mascot" -- that obviously means "school logo or school mascot" -- not *any* mascot.
"manufacturer's logo/trademark/reference" = "manufacturer's logo or manufacturer's trademark or manufacturer's reference"
That all being said... This is not a big deal and I wouldn't get hung up on it. Also, when in Rome...
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