I want to state that I cook on Mondays, Tue, Wed, Thur, and Fri, in my house every week. Should I say "I cook on Mondays to Fridays" or "I cook from Mondays to Fridays", or something else?
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Any of the following are OK, and synonymous:
As you can see, the first preposition is unnecessary, as is the plural.
If you insist on having two prepositions for some reason, from ... to and on ... through seem more likely to me, but that may be just my personal preference.
This is one of those constructions where there's a lot of possible choices that don't make any difference, as long as you avoid distractions. After all, it's such an expected situation that it gets abbreviated as just M-F most of the time.
Or you can spare yourself the trouble and just say:
I cook every day except on weekends/the weekend. (AE)
I cook every day except at weekends/the weekend. (BE)
There is a minor semantic difference:
'Cooking on Mondays to Fridays' allows that you may cook on Mondays to Fridays between 9am and 4pm
'Cooking from Mondays to Fridays' allows that you may cook from Monday to Friday (24hr continuously), for the Monday-to-Friday cycle of each and every week.
The latter is unlikely in context to the verb, but may be more than appropriate for other verbs, such as industrial manufacturing processes.