1. Thus , the optimal language up to this additive constant is universal .
2. Therefore , the optimal language is universal up to this additive constant .

yes

1. The result of these experiments led to the learning of processes for defining optimism .
2. The result of these experiments led to learning the processes of defining optimism .

yes

1. A module is called a serial module if it is a direct sum of modules .
2. A module is called a serial module if it is a direct sum of uniserial modules .
no