If A={a,1,-1,x} and B is another set such that the number of relation from A to B are 4096, then - Maths - Sets Relations and Functions

Question

If A={a,1,-1,x} and B is another set such that the number of
relation from A to B are 4096, then find the number of elements in
set B???

Ahmed Raza · Answer

Let the number of elements of set B be b
We know that,total number of subsets of A cross B is equal to total
number of relation from A to B Number of relation from A to B=total
no of subsets of A cross B=2 ^4*b Now according to question
2^4*b=4096 2^4*b=2^12 Bases are same so 4*b=12 b=3 and required no
of elements of set B is 3

If A={a,1,-1,x} and B is another set such that the number of relation from A to B are 4096, then find the number of elements in set B???