Hi Angliholic I'd use check in all three sentences. Look at the definitions for the word check . Basically, the meaning in all three of your sentences is 'examine'.
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AngliholicThanks, Yankee, for the reply and the link.
Nevertheless, I still don't quite understand the differences between "check on" and "check up on." Could I omit "up" in the following without making a change in meaning?
My mum checks up on me most evenings to see that I've done my homework.
By the way, could I say "investiga