Let W denote the words in the English dictionary. Define the relation R by :
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Given relation R such that
R = {(x, y) ε W × W | the word x and y have at least one letter in common} where W denotes set of words in English dictionary
Clearly (x ,x ) ε R for all x ε W
Therefore, (x, x) has every letter common, therefore R is reflexive
Let (x, y) ε R then (y, x) ε R as x and y have at least one letter in common, this implies, R is symmetric.
But R is not transitive, Let x = DON, y = NEST, z = SHE
R = {(x, y) ε W × W | the word x and y have at least one letter in common} where W denotes set of words in English dictionary
Clearly (x ,x ) ε R for all x ε W
Therefore, (x, x) has every letter common, therefore R is reflexive
Let (x, y) ε R then (y, x) ε R as x and y have at least one letter in common, this implies, R is symmetric.
But R is not transitive, Let x = DON, y = NEST, z = SHE
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Answer:
Reflexive,Symmetric But not transitive
Step-by-step explanation:
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