Questions: Hasil survei pada suatu kelas menunjukkan bahwa ada 8 siswa yang suka pelajaran matematika dan ada 10 siswa yang suka pelajaran ekonomi. Jika semua siswa suka minimal salah satu pelajaran tersebut, berapakah jumlah siswa dalam kelas tersebut? Putuskan apakah pernyataan 1 dan 2 berikut cukup untuk menjawab pertanyaan tersebut. 1. Ada 4 siswa yang suka pelajaran matematika saja. 2. Ada 4 siswa yang suka pelajaran matematika dan ekonomi. A Pernyataan 1 SAJA cukup untuk menjawab pertanyaan, tetapi pernyataan 2 SAJA tidak cukup. B Pernyataan 2 SAJA cukup untuk menjawab pertanyaan, tetapi pernyataan 1 SAJA tidak cukup. C DUA pernyataan BERSAMASAMA cukup untuk menjawab pertanyaan, tetapi SATU pernyataan SAJA tidak cukup. D Pernyataan 1 SAJA cukup untuk menjawab pertanyaan dan pernyataan 2 SAJA cukup.

Solution Steps

The problem states that in a class:

• 8 students like mathematics.
• 10 students like economics.
• All students like at least one of the two subjects.

We are asked to determine the total number of students in the class. Additionally, we are given two statements and need to decide whether they are sufficient to answer the question.

Let:

• \( M \) = number of students who like mathematics.
• \( E \) = number of students who like economics.
• \( M \cap E \) = number of students who like both mathematics and economics.
• \( M \cup E \) = total number of students in the class.

From the problem:

• \( M = 8 \)
• \( E = 10 \)
• All students like at least one subject, so \( M \cup E \) is the total number of students.

The principle of inclusion-exclusion states: \[ M \cup E = M + E - M \cap E \] We need to find \( M \cap E \) to determine \( M \cup E \).

Statement 1: "There are 4 students who like mathematics only."

This means: \[ M - M \cap E = 4 \] Given \( M = 8 \), we can solve for \( M \cap E \): \[ 8 - M \cap E = 4 \implies M \cap E = 4 \] Now, using the inclusion-exclusion principle: \[ M \cup E = 8 + 10 - 4 = 14 \] Thus, Statement 1 alone is sufficient to determine the total number of students.

Statement 2: "There are 4 students who like both mathematics and economics."

This directly gives: \[ M \cap E = 4 \] Using the inclusion-exclusion principle: \[ M \cup E = 8 + 10 - 4 = 14 \] Thus, Statement 2 alone is also sufficient to determine the total number of students.

Since both Statement 1 and Statement 2 are individually sufficient to answer the question, the correct option is: D. Pernyataan 1 SAJA cukup untuk menjawab pertanyaan dan pernyataan 2 SAJA cukup.

Final Answer