Consider a family $\mathcal{F}$ of subsets of $\{1, 2, \dots , n\}$ such that for any two distinct sets $A$ and $B$ in $\mathcal{F}$ we have: $A \subset B$ or $ B \subset A$ or $A \cap B = \emptyset$. Which of the following statements is TRUE? (Hint: what does the Venn diagram of this family look like?)
This is what I thought ..please correct if wrong ! $\text{Assuming } \;\;\ \{1, 2, \dots , 4\}$
With following recurrence relation:
$\begin{align*} f(n) = 2+ f(n-1) \;\; n\geq 2 \text{ and } \;\;\ f(1) = 2 \end{align*}$
64.3k questions
77.9k answers
244k comments
80.0k users