Given a non empty set X, 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 if A⊂B. Is R an equivalence relation on P(X)? Justify you answer:

Question

Given a non empty set X, 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 if A⊂B.  Is R an equivalence relation on P(X)? Justify you answer:

cdquestions Admin · Accepted Answer

Since every set is a subset of itself, ARA for all A ∈ P(X).  ∴R is reflexive.  Let ARB ⇒ A ⊂ B.  This cannot be implied to B ⊂ A.  For instance, if A = {1, 2} and B = {1, 2, 3},  then it cannot be implied that B is related to A.  ∴ R is not symmetric.  Further, if ARB and BRC,  then A ⊂ B and B ⊂ C.  $\Rightarrow$  A ⊂ C  $\Rightarrow$  ARC  ∴ R is transitive.  Hence, R is not an equivalence relation since it is not symmetric.

	LIST I		LIST II
A.	Range of y=cosec^-1x	I.	R-(-1, 1)
B.	Domain of sec^-1x	II.	(0, π)
C.	Domain of sin^-1x	III.	[-1, 1]
D.	Range of y=cot^-1x	IV.	\([\frac{-π}{2},\frac{π}{2}]\)-{0}

Given a non empty set X, 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 if A⊂B.
Is R an equivalence relation on P(X)? Justify you answer:

Solution and Explanation

Top Questions on Relations and Functions

Questions Asked in CBSE CLASS XII exam

Given a non empty set X, 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 if A⊂B. Is R an equivalence relation on P(X)? Justify you answer:

Solution and Explanation

Top Questions on Relations and Functions

Questions Asked in CBSE CLASS XII exam

Given a non empty set X, 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 if A⊂B.
Is R an equivalence relation on P(X)? Justify you answer: