Logic, like any other science, has as its business the pursuit of truth. What are true are certain statements and the pursuit of truth is the endeavor to sort out the true statements from the others, which are false.
Uh, no. Logic is there to check consistency between statements, which is only one aspect of the truth of a statement. Statements, in turn, are representations of situations, and both their adequacy and validity can be assessed separately. Further, anyone who uses the word "business" like that in the first sentence must be alerted to the existence, and slipperiness, of metaphors, which dominate communication, and are the key to understanding what "statements" can mean.
And if he begins so badly, can he rescue himself later?
Frankly, I can't be bothered.