My boyfriend says the phrases "Taste of this" and "Smell of this" often. I have tried to explain to him that these statements are incorrect and that "Taste this" or "Smell this" are more appropriate. He thinks his statements are correct but I can not explain to him why they are not. Can someone explain that to me.
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[Taste / Smell] of this is a regionalism. He may have been brought up in or near the Carolinas, for example. If he has heard it and said it that way all his life, of course he will insist that it is right. And within regions where it is used, it will also seem right to everyone else!
The more usual phrase used throughout the U.S. drops the of, treating taste and smell as transitive verbs that take direct objects.

The Merry Heart - Page 167
by Helen Abbott Beals, Century Company, Century Company - Fiction - 1918 - 351 pages

Here, just taste of this." As Belinda laid out some spicy cookies upon a plate
already waiting on the red-covered dining table, she bent closer to Anne. ...


English Plays of the Nineteenth Century: 1800-50 V. 1 - Page 276

by Michael R. Booth - Literary Criticism - 1976 - 328 pages

Just taste of this, my beauty! JENNY.

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thank you so much. it looks like i have egg on my face then. i was pretty insistent that the phrase was incorrect. thank you!
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It can be analyzed as a partitive. A taste isn't the consumption of the entire item, but a taste of only some of it. Hence Taste (some) of this.