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Question

Let W denote the words in the English dictionary. Define the relation R by R=x,yW×Wthewordsx,yhaveatleastoneletterincommon then R is.


A

reflexive, symmetric, and not transitive

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B

reflexive, symmetric, and transitive

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C

reflexive, not symmetric, and transitive

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D

not reflexive, symmetric, and transitive

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Solution

The correct option is A

reflexive, symmetric, and not transitive


Explanation for the correct answer:

Finding the characteristics of R:

Let y be a word, y has every letter in common.

So,

y,yR

Thus R is reflexive.

Let, x,yR x,y have at least one letter is common, similarly y,x have at least one letter is common.

Thus R is symmetric.

Let us assume, x=apple, y=tap, z=thing

Here,

x,yR,y,zRbutx,zR

Thus R is not transitive.

Hence, the correct option is A.


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