Could of vs could have

i am attempting to explain the difference between could of and could have and really don't know if i am explaining it correctly or not.

My example is: I could of picked up the praying mantis to observe it, but that might of hurt the mantis.

I believe that is incorrect and corrected I have: I could have picked up the praying mantic to observe it, but that might have hurt the mantis.

Could someone check this and make sure I am doing this correctly?  Any explanation would be greatly appreciated!!!

"Could of" is wrong, it does not exist. It is, however, easy to mix up "could have" and "could of", since it is normally pronounced  in a slurred way and then it sounds like "could of".

Zerox wrote:

"Could of" ... does not exist.

I suppose that has some paradoxical value.

/km

of ... is a preposition and is generally placed before a noun
eg.  she is part OF a group.  ( a group. the noun preceded by it's preposition)

could ... is an adverb which describes the verb
eg. she COULD be part OF the group ... (COULD describes the verb TO BE)

It follows from the above that the expression:

 COULD OF has no sensible grammatical meaning.... (ie. an ADVERB describing a PREPOSITION)

COULD HAVE is an adverb describing the verb (HAVE) which follows it; this has a sensible grammatical meaning.