b is correct. He isn't a good boy
Here are the rules for contractions:
Apostrophes with Verb Contractions
Apostrophes generally show missing letters in contractions. In most formal writing such contractions should be avoided.
The most common contractions involve verbs in five situations.
1. Verbs with not contracted, or shortened.
Examples: aren't don't isn't wasn't can't weren't weren't wouldn't doesn't hasn't haven't couldn't
Note: The word won't is a contraction of will not--in older dialects will was often spelled with an o. The word shan't for shall not is seldom used in the United States. The word ain't is considered nonstandard.
2. Pronouns with will.
Examples: I'll you'll he'll she'll they'll
Note: In conversation the word will is often slurred and may show up in dialogue as 'll after most nouns, e.g., "John'll come home soon."
3. Pronouns and nouns with the verb to be.
Examples: I'm you're who's (i.e., who is) he's she's it's we're they're
Note: In conversation the word is is often contracted with nouns, e.g. "Martha's here."
Please note four confusing contractions:
who's it's you're they're
Remember, the apostrophe indicates that letters have been left out.
who's = who is or who has you're = you are it's = it is or it has they're = they are
The possessive of who is whose.
Correct: Who's coming with me? (Contraction)
Correct: Whose book is this? (Possessive)
4. Pronouns with the verb to have.
Examples: I've he's you've we've they've
(Note that the 's could stand for is or has.)
Note: Sometimes the word have is slurred, especially after verbs like would, could, and should. In dialogue this can be shown as 've, but never as of.
Incorrect: We would of like to have gone.
Correct: We would've liked to have gone.
(To show contraction in speaking)
Correct: We would have liked to have gone.
(In more formal writing)
5. Pronouns with would or had contracted.
Examples: I'd he'd she'd you'd we'd they'd
I'd better go.
(I had better go.)
He'd want to go.
(He would want to go.)
In everyday conversation the word would is often slurred and may be shown as 'd following a noun in dialogue, e.g. "John'd be upset if he found out."