Question

If maximum number of relation on set A is 512 , then find the cardinal number of A.

Answer 1

If set A has m elements and B has n elements, then there are $2^{mn}$ different relations from A to B.
Since we have relation from set A to A therefore if the no of elements in set A (cardinal no ) is m then:
Total relations $=2^{(m\times m)}=512$
$=2^{(m\times m)}=2^9$
$m^2=9$
$m=3$