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
*R*_{1}
*A*_{1}
*A*_{2}
and
*R*_{2}
*B*_{1}
*B*_{2}
are **equal** if and only if
*A*_{1} = *B*_{1} , *A*_{2} = *B*_{2} ,
and ** ***R*_{1} = *R*_{2} as a set.

For example, let
**R**_{1} **= {<***1, 2*> , <*2, 2*>}
{*1, 2*}
{*1, 2*} ,
and
**R**_{2} ** = {<***a, b*> , <*b, b*>}
{*a, b*}
{*a, b*} .
Then *R*_{1} = *R*_{2} if and only if *a* = *1* and
*b* = *2*.

**Definition (equality of ***n*-ary relation):

An *n*-ary relation
*R*_{1}
*A*_{1}
...
*A*_{n}
and
an *m*-ary relation
*R*_{2}
*B*_{1}
...
*B*_{m}
are **equal**
if and only if *m* = *n*, *A*_{i} = *B*_{i}
for each *i*,
*1*
*i*
*n* , and
*R*_{1} = *R*_{2} 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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