Mortaza Hajhosseini has recently published the second edition of his book Two Non-Classical Logic Systems, A new Outlook on Elements of Logic. Similar to the first edition, he has introduced four non-classical logics (truth-functional, non-truth-functional and a combination of the two). In this article, I will only deal with his truth-functional system and the formal-mathematical criticisms levelled against it. I will leave the discussions related to the non-truth-functional system, as well as the philosophical and non-formal criticisms of both systems, and the related historical materials to a future article. The major formal criticisms are as follows: 1. the cyclic nature of some definitions; 2. Losing the rule of substitution; 3. The incorrect expression of the rules of reduction ad absurdum; 4. The lack of relationship between premises and conclusions of inferences; 5. Equivalence of formulas to several inequivalent ones; 6. Lack of correspondence between a condition with an inference. There are some less important criticisms: 7. Failure to express the rule of assumption; 8. Failure to state the reason for the lack of harmony in the rule of disjunction elimination in classical logic and the harmony of the disjunctive syllogism in the truth-functional system; 9. Expressing the rules of sub-proofs without using them.