Relation
Equality of Relations
Subjects to be Learned
- equality of binary relations
- equality of n-ary relations
Contents
Definition (equality of binary relation):
Two binary relations
R1
A1
A2
and
R2
B1
B2
are equal if and only if
A1 = B1 , A2 = B2 ,
and R1 = R2 as a set.
For example, let
R1 = {<1, 2> , <2, 2>}
{1, 2}
{1, 2} ,
and
R2 = {<a, b> , <b, b>}
{a, b}
{a, b} .
Then R1 = R2 if and only if a = 1 and
b = 2.
Definition (equality of n-ary relation):
An n-ary relation
R1
A1
...
An
and
an m-ary relation
R2
B1
...
Bm
are equal
if and only if m = n, Ai = Bi
for each i,
1
i
n , and
R1 = R2 as a set of ordered n-tuples.
Test Your Understanding of Equality of Relations
Indicate which of the following statements are correct and which are not.
Click True or False , then Submit. There is one set of questions.
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