저의: formal way to say "my". Contraction is 제. Less formal: 나의 ➡ 내.
Also 강아지 (gangaji) is another common way to say dog.
Well actually 강아지 is puppy. But then again i call ever dog puppy no matter how old.
Sometimes when there's two vowels next to each other in Korean (like when adding an ending to a word that also ends in a vowel), the two vowels contract so it's easier to say.
For example, instead if saying something like 행복하여요 (haengbokhayeoyo), which basically means "it is happy", the third and fourth syllables would contract to 행복해요 (haengbokhaeyo). It still means the same thing, it's just easier and smoother to say. There's quite a few different rules for conjugations of different character combinations (including some with consonants as well), but you don't really have to worry about most of them until later on. Just know that conjugating doesn't change the meaning, it just makes it easier to say. :)
A contractions is a shortest way to say a word... Like in English they are turns to they're to be just one syllable
Difference between "my" and "i am". Here are example sentences: 나는 개다 I am a dog. naneun gaeda. 내 강아지 My dog. nae gang-aji. (강아지 is another way to say "dog") "My" = "내", which is a contraction of "나의" - less formal "My" = "제", which is a contraction of "저의" - more formal. "I am" = "나는" naneun. And a more formal way to say “I am” = 저는 jeoneun.
Is 저의 a possessive pronoun (like in English) or is 의 a possessive particle (like in Japanese (の) / Chinese (的) ) and just adds to the subject?