I know from other discussions that Je ai is not the same as J'ai, but can someone explain why they are different?
As a general rule, when a word begins with an h or a vowel, shorten the word before it. e.g. l'oignon or j'ai
Yes, but don't think that because the French uses an apostrophe that it's informal. It's the only way to say "I have".
I've a cat isn't proper English. You dont use I've to use as possessive. Which one sounds better: I've a cat, or I have a cat?