Let W denotes the words in the English dictionary Define the relation R by R-x-y - W- W the ward x and y have at least one letter in common- Then R is

Explanation for the correct answer:The given relation is R={(x,y)∈ W× W} the words x and y have at least one letter in commonChecking for Reflexive Property:(a, ...

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Standard XIII

Mathematics

Condition for Concurrency of Three Lines

Let W denotes...

Question

Let $W$ denotes the words in the English dictionary Define the relation $R$ by $R = {(x, y) \in W \times W}$ the ward $x$ and $y$ have at least one letter in common. Then $R$ is

Not reflexive, symmetric, and transitive

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Reflexive, symmetric, and not transitive

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Reflexive, symmetric, and transitive

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Reflexive, not symmetric, and transitive

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Solution

The correct option is B
Reflexive, symmetric, and not transitive

Explanation for the correct answer:
The given relation is $R = {(x, y) \in W \times W}$ the words $x$ and $y$ have at least one letter in common
Checking for Reflexive Property:
$(a, a) \in R$
If $a \in W, a = R A M$ (say)
$R$ is reflexive
Checking for Symmetric Property:
$(R A M, A A M) \in R$
$(A A M, R A M) \in R$
If $(a 1, a 2) \in R$ and $(a 2, a 1) \in R$ , then $R$ is symmetric.
Checking for Transitive Property:
If $(a 1, a 2) \in R$ and $(a 2, a 3) \in R$ , then $(a 1, a 3) \in R$
$a 1 = R A M, (a 1, a 2) \in R a 2 = N A A M, (a 2, a 3) \in R a 3 = N O N E, (a 1, a 3) \notin R$
$R$ is not transitive.
Hence, the correct option is (B)

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Let W denotes the words in the English dictionary Define the relation R by R={(x,y)∈W×W} the ward x and y have at least one letter in common. Then R is

Let $W$ denotes the words in the English dictionary Define the relation $R$ by $R = {(x, y) \in W \times W}$ the ward $x$ and $y$ have at least one letter in common. Then $R$ is