Subjects set theory

Language Studies D6B2Fb

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1. **Problem statement:** In a class of 52 students, 30 study C++, 28 study Pascal, and 13 study both languages. We need to find how many students study at least one language and how many study neither. 2. **Formula used:** To find the number of students studying at least one language, use the principle of inclusion-exclusion: $$\text{At least one} = |C++| + |Pascal| - |C++ \cap Pascal|$$ 3. **Calculate students studying at least one language:** $$30 + 28 - 13 = 45$$ 4. **Calculate students studying neither language:** Total students minus those studying at least one: $$52 - 45 = 7$$ 5. **Answer:** - Number studying at least one language: 45 - Number studying neither language: 7