rel_is_reflexive {agop} | R Documentation |

## Reflexive Binary Relations

### Description

A binary relation `R`

is reflexive, iff
for all `x`

we have `xRx`

.

### Usage

```
rel_is_reflexive(R)
rel_closure_reflexive(R)
rel_reduction_reflexive(R)
```

### Arguments

`R` |
an object coercible to a 0-1 (logical) square matrix, representing a binary relation on a finite set. |

### Details

`rel_is_reflexive`

finds out if a given binary relation
is reflexive. The function just checks whether all elements
on the diagonal of `R`

are non-zeros,
i.e., it has `O(n)`

time complexity,
where `n`

is the number of rows in `R`

.
Missing values on the diagonal may result in `NA`

.

A reflexive closure of a binary relation `R`

,
determined by `rel_closure_reflexive`

,
is the minimal reflexive superset `R'`

of `R`

.

A reflexive reduction of a binary relation `R`

,
determined by `rel_reduction_reflexive`

,
is the minimal subset `R'`

of `R`

,
such that the reflexive closures of `R`

and `R'`

are equal
i.e., the largest irreflexive relation contained in `R`

.

### Value

The `rel_closure_reflexive`

and
`rel_reduction_reflexive`

functions
return a logical square matrix. `dimnames`

of `R`

are preserved.

On the other hand, `rel_is_reflexive`

returns
a single logical value.

### See Also

Other binary_relations:
`check_comonotonicity()`

,
`pord_nd()`

,
`pord_spread()`

,
`pord_weakdom()`

,
`rel_graph()`

,
`rel_is_antisymmetric()`

,
`rel_is_asymmetric()`

,
`rel_is_cyclic()`

,
`rel_is_irreflexive()`

,
`rel_is_symmetric()`

,
`rel_is_total()`

,
`rel_is_transitive()`

,
`rel_reduction_hasse()`

*agop*version 0.2.4 Index]