Let $A, B$ and $C$ be sets. Then show that $A\cap (B\cup C)=(A\cap B)\cup (A\cap C)$

Out of $100$ students; $15$ passed in English, $12$ passed in Mathematics, $8$ in Science, $6$ in English and Mathematics, $7$ in Mathematics and Science; $4$ in English and Science; $4$ in all the three. Find how many passed in English and Mathematics but not in Science

Out of $100$ students; $15$ passed in English, $12$ passed in Mathematics, $8$ in Science, $6$ in English and Mathematics, $7$ in Mathematics and Science; $4$ in English and Science; $4$ in all the three. Find how many passed in Mathematics and Science but not in English

Out of $100$ students; $15$ passed in English, $12$ passed in Mathematics, $8$ in Science, $6$ in English and Mathematics, $7$ in Mathematics and Science; $4$ in English and Science; $4$ in all the three. Find how many passed in Mathematics only

Out of $100$ students; $15$ passed in English, $12$ passed in Mathematics, $8$ in Science, $6$ in English and Mathematics, $7$ in Mathematics and Science; $4$ in English and Science; $4$ in all the three. Find how many passed in more than one subject only

In a town of$10,000$ families it was found that $40\%$ families buy newspaper $A$, $20\%$ families buy newspaper $B$, $10\%$ families buy newspaper $C$, $5\%$ families buy $A$ and $B$, $3\%$ buy $B$ and $C$ and  $4\%$ buy $A$ and $C$. If $2\%$  families buy all the three newspapers. Find the number of families which buy newspaper $A$ only.

In a town of$10,000$ families it was found that $40\%$ families buy newspaper $A$, $20\%$ families buy newspaper $B$, $10\%$ families buy newspaper $C$, $5\%$ families buy $A$ and $B$, $3\%$ buy $B$ and $C$ and  $4\%$ buy $A$ and $C$. If $2\%$  families buy all the three newspapers. Find the number of families which buy none of $A, B$ and $C$.