First slide

Relations XII

Question

Given a non empty set & consider P(X) which is the set of all subsets of X. Define the relation R in P(X) as follows:
For subsets A, B in P(X), ARB if and only it A $\subset$ B. Then R is not

Easy

A

Reflexive
B

Transitive
C

Symmetric
D

All the above

Solution

$Since every set is a subset of itself, A R A for all A \in P (X)$
Therefore, .R is reflexive.
$\begin{array}{l} Let A R B \Rightarrow A \subset B . \\ This cannot be implied to B \subset A . \end{array}$
$For instant, if A = {1, 2} and B = {1, 2, 3}, then it cannot be$
implied that B is related to A.
Therefore, R is not symmetric.
$Further if A R B and B R C, then A \subset B and B \subset C .$
$\begin{aligned} \Rightarrow A \subset C \\ \Rightarrow A R C \end{aligned}$
Therefore, R is transitive. Hence, R is not an equivalence relation since it is not symmetric

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App