Subjects set theory

Math Only

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Math Only


1. **State the problem:** We have a class of 40 students. - 25 study Mathematics. - 20 study English. - 10 study both Mathematics and English. We need to find how many students study Mathematics only. 2. **Understand the sets:** - Let $M$ be the set of students studying Mathematics. - Let $E$ be the set of students studying English. We know: $$|M| = 25, \quad |E| = 20, \quad |M \cap E| = 10$$ 3. **Find Mathematics only:** Students studying Mathematics only are those in $M$ but not in $E$: $$|M \setminus E| = |M| - |M \cap E| = 25 - 10 = 15$$ 4. **Answer:** The number of students who study Mathematics only is **15**. Therefore, the correct choice is **c. 15**.