I am struggling figureing a couple of these answers out for Discrete Mathematics

Question

I am struggling figureing a couple of these answers out for Discrete Mathematics and Its Applications.

1. n is an integer. n is positive. Therefore n is a positive integer A. Addition B. Invalid argument. O C. Simplification D. Disjunctive syllogism. E. Conjuction. F. Modus ponens. O G. Hypothetical syllogism. 2. I can answer all the exercises if I work all night on this homework. If I answer all the exercises, I will understand the material. Therefore, I will understand the material. if I work all night on this homework. A. Modus tollens. B. Conjuction. C. Addition D. Invalid argument. E. Modus ponens. F. Disjunctive syllogism. o G. Hypothetical syllogism.

Explanation / Answer

1. Its a conjuction because here we combined 2 statements into one

2. its also a conjuction because here we are combining 3 statements and we dont use any implication there and hence i feel conjuction is a better choice among given options

3. Its just simplification because we are already given p and q and from here we deduce q and its just a normal simplification.

4. Yes its an invalid statement because use cannot use and to combine a new statement with already proven one.

5. yes its an fallacy of assuming conclusion

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