Let $ P(S) $ denote the power set of $ S=\{1,2,3, \ldots, 10\} $. Define the relations $ R_{1} $ and $ R_{2} $ on $ P(S) $ as $ A R_{1} B $ if $ \left(A \cap B^{C}\right) \cup\left(B \cap A^{C}\right)=\phi $ and $ A R_{2} B $ if $ A \cup B^{C}=B \cup A^{C}, \forall A, B \in P(S) $. Then

Only $ R_{2} $ is an equivalence relation

Both $ R_{1} $ and $ R_{2} $ are not equivalence relations

Only $ R_{1} $ is an equivalence relation

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JEE MATHEMATICS MCQ: SET THEORY

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Analyzing +4 | -1

Let

P(S)

denote the power set of

S=\{1,2,3, \ldots, 10\}

. Define the relations

R_{1}

and

R_{2}

P(S)

A R_{1} B

\left(A \cap B^{C}\right) \cup\left(B \cap A^{C}\right)=\phi

and

A R_{2} B

A \cup B^{C}=B \cup A^{C}, \forall A, B \in P(S)

. Then

View answer and explanation

Correct option: D

Both

R_{1}

and

R_{2}

are equivalence relations

Option D is correct. Both

R_1

and

R_2

are equivalence relations because they both imply

A=B

More Questions from SET THEORY

Practice All Chapter MCQs →

Let

S

be the set of all those 2007-place decimal integers

2 a_1 a_2 a_3 \ldots . . a_{2006}

which contain odd number of digit 9 in each sequence

a_1, a_2, a_3, \ldots ., a_{2006}

. The cardinal number of

S

is If

a N=\{a n: n \in N: b N=\{n b: n \in N\}

c N=\{c N: n \in N\}

and

b N \cap c N=d N

, where

a, b, c \in N

and

b, c

are coprime, then Which of the following cannot be the number of elements in the power set of any finite set? If

A=\{x: x

is a multiple of 3

\}

and

B=\{x: x

is a multiple of 5}, then

A-B

is equal to If

F(n)

denotes the set of all divisors of

n

except 1 , what is the least value of y satisfying

[\mathrm{F}(20) \cap \mathrm{F}(16)] \subseteq \mathrm{F}(\mathrm{y})

? In a town of 10000 families, it was found that

40 \%

families buy newspaper

A, 20 \%

families buy newspaper B and

10 \%

families buy newspaper

C

, 5% families buy newspapers

A

and B, 3% buy newspapers B and

C

and

4 \%

buy newspapers

A

and

C

. If

2 \%

families buy all the three newspapers, then number of families which buy

A

only is