Let 
. Then the number of one-one functions 
, where 
denote the power set of 
, such that 
where 
is
Text Solution
Verified by Experts3240
(3240)
Case - I
i.e. 1 option
any 5 element subset 
of 
i.e. 
options
any 4 element subset 
of 
i.e. 
options
any 3 element subset 
of 
i.e. 
options
any 2 element subset 
of 
i.e. 
options
any 1 element subset 
of 
or empty subset i.e. 3 options
Total function 
Case - II
any 4 element subset 
of 
i.e. 
options
any 3 element subset 
of 
i.e. 
options
any 2 element subset 
of 
i.e. 
options
any 1 element subset 
of 
i.e. 
options
empty subset i.e. 1 options
Total function 
Case - III
any 5 element subset 
of 
i.e. 
options
any 3 element subset 
of 
i.e. 
options
any 2 element subset 
of 
i.e. 
options
any 1 element subset 
of 
i.e. 
options
empty subset i.e. 1 options
Total function 
Case - IV
any 5 element subset 
of 
i.e. 
options
any 4 element subset 
of 
i.e. 
options
any 2 element subset 
of 
i.e. 
options
any 1 element subset 
of 
i.e. 
options
empty subset i.e. 1 options
Total function 
Case - V
any 5 element subset 
of 
i.e. 
options
any 4 element subset 
of A i.e. 
options
any 3 element subset 
of 
i.e. 
options
any 1 element subset 
of 
i.e. 
options
empty subset i.e. 1 options
Total function 
Case - VI
any 5 element subset 
of 
i.e. 
options
any 4 element subset 
of A i.e. 
options
any 3 element subset 
of 
i.e. 
options
any 2 element subset 
of 
i.e. 
options
any 1 element subset 
of 
i.e. 
options
empty subset i.e. 1 options
Total function 
Total number of such functions 
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems