60 votes 60 votes Let ܵ$S$ denote the set of all functions $f:\{0,1\}^4 \to \{0,1\}$. Denote by $N$ the number of functions from S to the set $\{0,1\}$. The value of $ \log_2 \log_2N $ is _______. Set Theory & Algebra gatecse-2014-set1 set-theory&algebra functions combinatory numerical-answers + – go_editor asked Sep 28, 2014 retagged Jun 27, 2017 by Arjun go_editor 12.4k views answer comment Share Follow See all 3 Comments See all 3 3 Comments reply Vysakh Remesh commented Jul 12, 2020 reply Follow Share The beauty of the question hovers around the set $S$. 10 votes 10 votes Mohitdas commented Dec 15, 2021 reply Follow Share ……………….. 5 votes 5 votes tusharb commented Jan 9, 2022 reply Follow Share If anyone is wondering what {0,1}^4 means, it is actually the cartesian product {0,1}x{0,1}x{0,1}x{0,1}.={0000,0001…..} 10 votes 10 votes Please log in or register to add a comment.
4 votes 4 votes $f:\{{0,1}\}^4→\{0,1\} $ $\{0,1\}^4$ contains total $24$ elements so $16$ elements and S will be $[co-domain]^{domain} = 216$ $\text{N is S to } \{0,1\} \text { so } 2^{216}$ $log_2log_2N = 16$ Rishi yadav answered Oct 12, 2017 edited Dec 15, 2018 by Rishi yadav Rishi yadav comment Share Follow See 1 comment See all 1 1 comment reply Apoorva Jain commented Dec 15, 2018 reply Follow Share Great explanation about boolean functions of n variables. https://cs.fit.edu/~wds/classes/adm/Lectures/BooleanFunctions.pdf 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes . NOTE here N = Number of functions from S to set {0,1} i.e 2^S akshay_123 answered Sep 27, 2023 akshay_123 comment Share Follow See all 0 reply Please log in or register to add a comment.