Given a non empty set X

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

3. Given a non empty set X , consider

\mathrm{P}(\mathrm{X})

which is the set of all subsets of X . Define the relation

R

P(X)

as follows: For subsets

\mathrm{A}, \mathrm{B}

\mathrm{P}(\mathrm{X}), \mathrm{ARB}

if and only if

\mathrm{A} \subset \mathrm{B}

. Is R an equivalence relation on

\mathrm{P}(\mathrm{X})

? Justify your answer.