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Let F be the set of all human beings in town in a particular t

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Let $F$ be the set of all human beings in town in a particular time. Then check whether the relation is as equivalence relation.
$R = {(x, y) : x is mother of y}$ .

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Let

F

be the set of all human beings in town in a particular time. Then check whether the relation is as equivalence relation.

R = {(x, y) : x is mother of y}

14 mins ago

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14 mins ago

Text solutionVerified

The relation is not reflexive as

(x, x) \neq \in R

for any

x \in F

since

x

can't be its own mother.

Similarly the relation is not symmetric as if

(x, y) \in R

this does not give

(y, x) \in R

since if

x

is mother of

y

this does not mean that

y

is also mother of

x

for any

x, y \in F

Again this relation

R

is not transitive as if

(x, y) \in R, (y, z) \in R

this does not give

(x, z) \in R

for any

x, y, z \in F

So this relation is not equivalance.

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Question Text	Let $F$ be the set of all human beings in town in a particular time. Then check whether the relation is as equivalence relation. $R = {(x, y) : x is mother of y}$ .
Answer Type	Text solution:1
Upvotes	150

Let F be the set of all human beings in town in a particular time. Then check whether the relation is as equivalence relation.R={(x,y):x is mother of y}.

Text solutionVerified

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Let $F$ be the set of all human beings in town in a particular time. Then check whether the relation is as equivalence relation.
$R = {(x, y) : x is mother of y}$ .