According to conflict serializability WRITE
operation conflicts both with READ
and WRITE
operations. Therefore, even though each READ (A)
does not conflict with the other one, it does with the WRITE (A)
instruction of the other transaction.
For a deeper explanation, you could consider checking "Database System Concepts", by Abraham Silberschatz et. al. The chapter 14.6 of the 6th edition should be clarifying.
EDIT: Based on what I said before, and adding that a schedule is conflict-serializable if, and only if, it can be derived from a serial one (no pair of transactions can be executed in parallel) swapping the order of pairs of instructions which are not conflicting with each other, it is evident that the effect of conflict-serializable schedules on any database will be equivalent to this of serial ones. Therefore, we can conclude that conflict serializability grants consistency.
Being that said, database managers can implement this kind of scheduling or not, with the corresponding effect on consistency of transactions.