1. **Problem Statement:** Given a Venn diagram representing students who passed in Mathematics, Science, and Tamil subjects with a total of 80 students. 2. **Known values from the Venn diagram:** - Total students $= 80$ - Students passed in Mathematics only $= 5$ - Students passed in Science only $= 9$ - Students passed in Tamil only $= 12$ - Students passed in Mathematics and Science only $= 5$ - Students passed in Science and Tamil only $= 4$ - Students passed in Mathematics and Tamil only $= 0$ (not given, assume 0) - Students passed in all three subjects $= 10$ - Students outside all three subjects $= 8$ 3. **Formula used:** For three sets $M$, $S$, and $T$, the total number of elements is given by: $$|M \cup S \cup T| = |M| + |S| + |T| - |M \cap S| - |S \cap T| - |M \cap T| + |M \cap S \cap T|$$ 4. **Calculate total students passed in Science:** Science students include those who passed only Science, Science and Mathematics, Science and Tamil, and all three. $$|S| = 9 + 5 + 4 + 10 = 28$$ 5. **Calculate students passed in Mathematics or Science:** $$|M \cup S| = |M| + |S| - |M \cap S|$$ Where: - $|M| = 5 + 5 + 0 + 10 = 20$ - $|S| = 28$ (from step 4) - $|M \cap S| = 5 + 10 = 15$ So, $$|M \cup S| = 20 + 28 - 15 = 33$$ **Final answers:** - (ii) Number of students passed in Science $= 28$ - (iii) Number of students passed in Mathematics or Science $= 33$