# DM - Functions & Relations -Q19

+1 vote

Let "Closure of a Relation R with respect to a Property P" be defined as follows:

let R be a relation on a set A. Then a relation R' is the closure of the relation R with respect to property P if and only if

1. R' satisfy the property P, and

2. , and

3. for any(every) relation R'' if and satisfies the property R, then

i.e if there is a relation R' with property P containing R such that R' is a subset of every relation R'' with property P containing R, then R' is called the closure of R with repect to P

Let  relation R on a set

Let the property "P" be "has an odd number of elements".

The closure of R with respect to property P is :

(A).

(B).

(C).

(D). None of these asked Jun 24
edited 3 days ago

Let the property "P" be "has an odd number of elements".

Let  relation R on a set

Since R doesn't have property P so we have to add something to it and make R' that willl satisfy property P.

The closure of R with respect to property P is :

(A).

This doesn't have property P. So, False.

(B).

This has property P BUT  Other relation R'' with property P is also possible such that R'' is Not a superset of R' and R'' also covers R and satisfies P. For example,

So, this is also false and we can now see that No such closure exists w.r.t. this given property for this given relation. answered 3 days ago by (112,390 points)