Select all that apply

Consider the following systems specification. If the transaction has an exclusive lock on the database element, then it can modify and read the element. If the transaction has a shared lock on the database element, then it can read the element, but can not modify it$.$ The transaction either has an exclusive lock or a shared lock on the database element.

Let s be the proposition: "The transaction has a shared lock on the database element," e: "The transaction has an exclusive lock on the database element," m: "The transaction can modify the database element," and r: "The transaction can read the database element."

The translation of the specification into propositional logic is as follows:

e $->($r $$ m$)$

s $->($r $$m$)$

$($e $$ s$)($e $$ s$)$

Which of the following additions to the specification make it inconsistent.

Multiple select question.

The transaction cannot modify the database element.

The transaction does not have a shared lock and cannot modify the database element.

The transaction does not have an exclusive lock and cannot modify the database element.

The transaction cannot read the database element.