For this question, we clearly need to understand, the token , lexeme and pattern
Lexeme: Lexeme is a sequence of character, that matched with pattern.
Pattern: Pattern is a sets of rule, that is form of accepted. i.e. letter(letter+digit)*
From ullman
"A lexeme is a sequence of characters in the source program that matches the pattern for a token and is identified by the lexical analyzer as an instance of that token."
"A token is a pair consisting of a token name and an optional attribute value. The token name is an abstract symbol representing a kind of lexical unit, e.g., a particular keyword, or sequence of input characters denoting an identifier. The token names are the input symbols that the parser processes."
"A pattern is a description of the form that the lexemes of a token may take. In the case of a keyword as a token, the pattern is just the sequence of characters that form the keyword. For identifiers and some other tokens, the pattern is more complex structure that is matched by many strings."
For example
Say for
int a;
DFA constructed from i, then n and then t, atlast got white-space, where i, n, t are lexeme
When it got white-space , "int" already matched with pattern. So, this token is accepted
So, here $S_{1}$ is just definition of grammar , Hence it is false.
But $S_{2}$ is true.