Logic or Math

Logic says that;

No Study = Fail ------------- (1)
Study = No Fail --------- (2)

According to Maths;

Adding (1) and (2) we get;

No Study + Study = Fail + No Fail

Taking common out on both sides, we get;

Study (No+1) = Fail (No+1)

Cancelling (No+1) from both the sides, finally we get

Study = Fail

If the above interpretations are true, whom should we believe . . . Logic or Maths?