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Let R be a relation defined as aRb if 1 + ab > 0, then the rel

Question

Let $R$ be a relation defined as $a R b$ if $1 + ab > 0$ , then the relation $R$ is:

Reflexive and symmetric

Symmetric but not reflexive

Transitive

Equivalence

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Eleanor Discussed

Let

R

be a relation defined as

a R b

1 + ab > 0

, then the relation

R

is:

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

Given relation is

a R b

1 + ab > 0

considering both

a

and

b

are real numbers,

We know that

ab = ba

⟹ a R b = 1 + ab > 0 = 1 + ba > 0 = b R a

∴

R

is a symmetric relation,

a R a = 1 + a^{2}

a^{2}

is always a positive real number,

∴ 1 + a^{2} > 0

∴

R

is a reflexive relation.

Consider

a R b

which is

1 + ab > 0

and also

b R c

which is equal to

1 + b c > 0

a = 0.5

and

b = - 0.5

and

c = - 4

⟹

both

a R b

and

b R c

are satisfied,

a R c = 1 - 2 < 0

∴

a R c

is not a realation,

Hence

R

is not a equivalence relation,but is a reflexive and symmetric relation.

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Question Text	Let $R$ be a relation defined as $a R b$ if $1 + ab > 0$ , then the relation $R$ is:
Answer Type	Text solution:1
Upvotes	150

Let R be a relation defined as aRb if 1+ab>0, then the relation R is:

Text solutionVerified

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Let $R$ be a relation defined as $a R b$ if $1 + ab > 0$ , then the relation $R$ is: