He is vegetarian; you won't get
meat at his house

An indefinite article is used when we are talking generally about something whereas a definite article is used when we are talking about something specific.

The indefinite articles are 'a' and 'an'. An is used before a word starting with a vowel or vowel sound. A is used before a word starting with a consonant or consonant sound.

A definite article is an article that tells the uniqueness of something.

'The' is the only definite article.

The first blank shall take the article 'a' because vegetarian starts with the consonant 'v' and is a singular countable noun while the second blank will not take any article as meat is an uncountable noun.

He is a vegetarian. He doesn't eat meat.

my dad purchased natural colorings in a specialty store

i think it would be c. or a. i recommend a if it's not a than it's c if it's not c than it's b your welcome : ) sorry if you get it wrong