Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Let
A
A
A
be a set with
n
n
n
elements. (i) State the condition that a relation
R
R
R
on
A
A
A
must satisfy to be symmetric. (ii) Prove that the total number of symmetric relations on
A
A
A
is
2
n
(
n
+
1
)
2
2^{\frac{n(n+1)}{2}}
2
2
n
(
n
+
1
)
. (iii) Find the number of symmetric relations when
n
=
3
n=3
n
=
3
.
Browse the problem library