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Grade: 11

                        

If R is a relation from asset P to set Q,then? R......

6 months ago

Answers : (2)

Arun
24742 Points
							
Dear student
 
A relation is akways a subset of ordered pair from p to q i.e. P x Q
 
Hence option A is correct.
 
Hope it helps
 
Thanks and regards
6 months ago
Vikas TU
12276 Points
							
R={(P,Q):distance of point P from the origin is the same as the distance of point Q from the origin}
Clearly, (P,P)∈R since the distance of point P from the origin is always the same as the distance of the same point P from the origin.
∴R is reflexive.
Now, let (P,Q)∈R.
⇒ the distance of point P from the origin is the same as the distance of point Q from the origin.
⇒ The distance of point Q from the origin is the same as the distance of point P from the origin.
⇒(Q,P)∈R
∴R is symmetric.
Now, let (P,Q),(Q,S)∈R.
⇒ The distance of points P and Q from the origin is the same and also, the distance of points Q and S from the origin is the same.
⇒ The distance of points P and S from the origin is the same.
⇒(P,S)∈R.
∴R is  transitive.
Therefore, R is an equivalence relation.
The set of all points related to P 
 =(0,0) will be those points whose distance from the origin is the same as the distance of point P  from the origin.
In other words, if O(0,0) is the origin and OP=k, then the set of all points related to P is at a distance of k from the origin.
Hence, this set of points forms a circle with the centre as the origin and this  circle passes through point P.
6 months ago
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