Functions Question 733
Question: Let S be any set and P (S) be its power set, We define a relation R on P(S) by ARB to mean $ A\subseteq B;\forall A,B\in P(S). $ Then R is
Options:
A) Equivalence relation
B) Not an equivalence but partial order relation
C) Both equivalence and partial order relation
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] (i) $ A\subseteq Aie,ARA,\forall A\in P(S) $
$ \therefore $ R is reflexive. (ii) $ A\subseteq BB\subseteq A $
$ \therefore ARBBRA $ . So R is not symmetric. (iii) ARB and BRA
$ \Rightarrow A\subseteq B $ and $ B\subseteq A\Rightarrow A=B $ Thus, R is anti-symmetric. (iv) ARB and BRC
$ \Rightarrow A\subseteq BandB\subseteq C $
$ \Rightarrow A\subseteq C\Rightarrow ARC $
$ \therefore $ R is transitive relation. Thus, R is partially ordered relation but not an equivalence relation.
BETA
