TIFR-2016-Maths-A: 16

Question

Let $S$ be a collection of subset of $\left \{ 1,2,\dots,100 \right \}$ such that the intersection of any two sets in $S$ is non-empty. What is the maximum possible cardinality $\left | S \right |$ of $S$ ?

• A. $100$
• B. $2^{100}$
• C. $2^{99}$
• D. $2^{98}$

Comments

https://math.stackexchange.com/questions/1573607/s-be-a-collection-of-subsets-of-1-100-any-two-sets-in-s-has-non