Sets, Relations & Functions
One-One Functions to Power Set
nta_pyq_2023_jan
Grade 11

Question:

Let $S = \{1,2,3,4,5,6\}$. Then the number of one-one functions $f: S \to P(S)$, where $P(S)$ denotes the power set of $S$, such that $f(n) \subset f(m)$ where $n < m$ is ______.

Step-by-Step Solution

Key Concept: Count chains of strictly increasing subsets; partition by $f(6)=S$ or proper subsets and enumerate cases.
Summing all cases: $1080+720+360+360+360+360=3240$.
Correct Answer: 3240

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