What great examples!
As for the last set of sentences: I'd call them just about interchangeable, except that "a lot" would be regarded as less formal. (NOAD tags "a lot" as "informal," e.g.) If I was proofreading my own writing, I'd probably change "I don't know a lot about" to "I don't know much about." Either would be fine in conversation, though.
I don't know much about Western history. {okay}
I don't know a lot about Western history. {okay in conversation, perhaps a bit informal for writing}
As for the middle set: I'd rephrase the latter sentence to read, "I don't watch a lot of TV." The first one could also be rephrased ("I don't watch very much TV"), but those two sentences have slightly different meanings: "I don't watch TV very much" would probably be interpreted as "I don't watch TV very often"; while "I don't watch very much TV" sounds more like "I don't watch many TV programs". The difference is very subtle, but I think it's existent. If I watched a half hour of TV nightly, but always the same program, I'd be inclined to say, "I don't watch a lot of TV," but not, "I don't watch TV very much." (After all, I watch nightly!)
I don't watch TV very much. {you don't watch TV very often}
I don't watch a lot of TV. {you don't watch too many TV programs}
I don't watch TV a lot. {not wrong per se, but I'd recommed one of the others}
As for the first set, that latter sentence sounds off to me. Interestingly enough, I have no problem with its inverse: "I like Japanese food a lot." However, when speaking in the negative, "I don't like Japanese food very much" sounds much more polished than "I don't like .. a lot."
I don't like Japanese food very much.
I don't like Japanese food a lot. {use the first one, not this one}
I like Japanese food very much.
I like Japanese food a lot. {in the positive, you can use either one}
I'm marveling how, even though the three pairs of examples all have the same sentence structure, my comments are different for all three. I guess this is a trickier problem than one might first expect.
Approbate means "to officially authorize" while approve means "agree or accept". Approbate is very formal and rather uncommon, and is usually used in official contexts such as political proceedings. Additionally, approbate refers more to the action of approving whereas approve connotes an attitude or sentiment, especially a moral judgment. Approve can also be used in context to mean "officially approve".
Examples:
"I don't approve of such revealing clothing."
"The chairman approbated our request."
"This order needs to be approved by a judge before it can be carried out."
Best Answer
The following in an extract from an interesting piece by M-W about the difference in usage and meaning between jealous and envious in which they state that despite the two terms tend to overlap in usage, there is a difference in the meaning they carry, as explained below:
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