Answer:
A. Determiner
Explanation:
To answer this question we need to understand what determiner is.
A determiner is a word that introduces a noun. It always comes before a noun, not after; it can come before an adjective used to describe the noun.
<u>There are 4 main types of determiners: articles, demonstratives, quantifiers, and possessives.</u>
<u>A</u> cat is a good pet - <u>determiner-article</u>
<u>These</u> black raspberries are sour - <u>determiner-demonstrative</u>
He ate <u>all</u> the cookies - <u>determiner-quantifier</u>
It's <u>our</u> secret recipe - <u>determiner-possessive</u>
As for our sentence - <em>These bagels are stale</em> - the word <u>'these' </u>is a determiner (demonstrative pronoun).
Demonstrative pronouns are also used as determiners in English. There are four of them: this, that, these and those. Demonstratives are used in a situation in which the speaker can point to the item they mean, making them even more specific than a definite article.
To sum up, the word <u>'these'</u> is a demonstrative pronoun and we can think option B is correct as it is a pronoun; but exactly in this sentence, <u>it is a pronoun that plays a role of a determiner. </u>
I hope it helped you :)