0000:00:00:00:00Start9Number 9ExplanationStudents will achieve high exam scores if they study very hard. This condition occurs when students can manage their time well. Which of the following conclusions is TRUE?Students who do not achieve high exam scores mean they cannot manage their time wellStudents do not achieve high exam scores if they can manage their time wellStudents can achieve high exam scores if they cannot manage their time wellStudents can manage their time well if they can achieve high exam scoresStudents who do not manage their time well will be able to achieve high exam scoresExplanationWe can solve this problem using syllogistic logic. Let's first define the premises: PPP: Students manage their time well. QQQ: Students study very hard. RRR: Students achieve high exam scores. Analyzing Premises Based on the text, we derive the following implications: "Students will achieve high exam scores if they study very hard" can be written as Q→RQ \rightarrow RQ→R. "This condition (studying hard) occurs when students can manage their time well" can be written as P→QP \rightarrow QP→Q. Drawing a Conclusion By combining these two premises, we get a logical chain: P→Q→R ⟹ P→RP \rightarrow Q \rightarrow R \implies P \rightarrow RP→Q→R⟹P→R The initial conclusion is: "If students can manage their time well, then they will achieve high exam scores." Logical Equivalence (Contrapositive) In mathematical logic, an implication statement P→RP \rightarrow RP→R is equivalent to its contrapositive, which is ∼R→∼P\sim R \rightarrow \sim P∼R→∼P. ∼R→∼P\sim R \rightarrow \sim P∼R→∼P This translates to: "If students do NOT achieve high exam scores, then they can NOT manage their time well." This statement matches the option stating that students who do not achieve high exam scores mean they cannot manage their time well. Remember the principles of Modus Tollens and Contrapositive: If A→BA \rightarrow BA→B is true, then ∼B→∼A\sim B \rightarrow \sim A∼B→∼A must also be true.
9Number 9ExplanationStudents will achieve high exam scores if they study very hard. This condition occurs when students can manage their time well. Which of the following conclusions is TRUE?Students who do not achieve high exam scores mean they cannot manage their time wellStudents do not achieve high exam scores if they can manage their time wellStudents can achieve high exam scores if they cannot manage their time wellStudents can manage their time well if they can achieve high exam scoresStudents who do not manage their time well will be able to achieve high exam scoresExplanationWe can solve this problem using syllogistic logic. Let's first define the premises: PPP: Students manage their time well. QQQ: Students study very hard. RRR: Students achieve high exam scores. Analyzing Premises Based on the text, we derive the following implications: "Students will achieve high exam scores if they study very hard" can be written as Q→RQ \rightarrow RQ→R. "This condition (studying hard) occurs when students can manage their time well" can be written as P→QP \rightarrow QP→Q. Drawing a Conclusion By combining these two premises, we get a logical chain: P→Q→R ⟹ P→RP \rightarrow Q \rightarrow R \implies P \rightarrow RP→Q→R⟹P→R The initial conclusion is: "If students can manage their time well, then they will achieve high exam scores." Logical Equivalence (Contrapositive) In mathematical logic, an implication statement P→RP \rightarrow RP→R is equivalent to its contrapositive, which is ∼R→∼P\sim R \rightarrow \sim P∼R→∼P. ∼R→∼P\sim R \rightarrow \sim P∼R→∼P This translates to: "If students do NOT achieve high exam scores, then they can NOT manage their time well." This statement matches the option stating that students who do not achieve high exam scores mean they cannot manage their time well. Remember the principles of Modus Tollens and Contrapositive: If A→BA \rightarrow BA→B is true, then ∼B→∼A\sim B \rightarrow \sim A∼B→∼A must also be true.
