What are the synonyms for their?

Both are correct.

Synonym means: a word having the same or nearly the same meaning as another in the language. Definition means: the act of defining or making definite, distinct, or clear / the formal statement of the...

The word no can be replaced in some contexts by none, negative, zero, or nothing.

He is a pronoun. The only synonym it has is to use the name of the person it refers to, i.e., "He is short." "John is short."

live, exist, survive, breathe, endure