3 Prove that the conclusionderived from the followingproposition is valid either logicis difficult to learn or a fewstudents dont like it; Ifmathematics is easy to learnlogic is not difficult to learnTherefore logic mathematics isnot difficult to learn

To prove the validity of the conclusion, we can use a proof by contradiction.

Assume that logic and mathematics are both difficult to learn. This means that the first premise "either logic is difficult to learn, or a few students don't like it" is true, as logic is difficult to learn. Additionally, the second premise "if mathematics is easy to learn, logic is not difficult to learn" is false, as mathematics is easy to learn but logic is still difficult to learn.

However, this contradicts the conclusion "logic, mathematics is not difficult to learn." Therefore, our assumption that logic and mathematics are both difficult to learn must be false.

We can conclude that either logic is not difficult to learn or a few students don't like it. And since mathematics is easy to learn, logic is not difficult to learn. Therefore, the conclusion that "logic, mathematics is not difficult to learn" is valid.