TIFR CSE 2016 | Part A | Question: 8

Question

Let $A$ and $B$ be finite sets such that $A \subseteq B$. Then, what is the value of the expression:

$$ \sum \limits_{C:A \subseteq C \subseteq B} (-1)^{\mid C \setminus A \mid,}$$

Where $C \setminus A=\{x \in C : x \notin A \}$?

• A. Always $0$
• B. Always $1$
• C. $0$ if $A=B$ and $1$ otherwise
• D. $1$ if $A=B$ and $0$ otherwise
• E. Depends on the size of the universe

Answer 1

Correct option is (D) 1 if A=B and 0 otherwise

Comments

Why in my example odd and even terms are not equal  according to formula ?