Have you seen water flowing unnecessarily in your home, school or any other place? Where?
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Solution

Disclaimer: This is a sample answer. The answer may vary from student to student, depending upon his/her observation and experience.

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For any two sets A and B, prove that

(i) $(A \cup B) - B = A - B$

(ii) $A - (A \cap B) = A - B$

(iii) $A - (A - B) = A \cap B$

(iv) $A \cup (B - A) = A \cup B$

(v) $(A - B) \cup (A \cap B) = A$

(A \cup B) - B = A - B

A - (A \cap B) = A - B

A - (A - B) = A \cap B

A \cup (B - A) = A \cup B

(A - B) \cup (A \cap B) = A

A

B,

A - (A \cap B)

a_{1}, a_{2}, a_{3}, a_{4}

1 + x)^{n}

\frac{a_{1}}{a_{1} + a_{2}} + \frac{a_{3}}{a_{3} + a_{4}} =

A (- a, - a), B (a, - a), C (- a, a), D (- a, a)

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