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Let W denote the words in the English dictionary. Define the relation R by R = {(x, y) ∈ W × W| the words x and y have at least one letter in common}. Then, R is
  • a)
    reflexive, symmetric and not transitive
  • b)
    reflexive, symmetric and transitive
  • c)
    reflexive, not symmetric and transitive
  • d)
    not reflexive and symmetric
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Let W denote the words in the English dictionary. Define the relation ...
Let W = {CAT, TOY, YOU, ……..)
Clearly, R is reflexive and symmetric but not transitive.
Since, CATRTOY, TOYRYOU ⇒ CATRYOU
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Most Upvoted Answer
Let W denote the words in the English dictionary. Define the relation ...
Reflexive Property:
- The relation R is not reflexive because there are words in the English dictionary that do not share any common letters with themselves, such as "apple" and "orange".

Symmetric Property:
- The relation R is symmetric because if x has a common letter with y, then y also has a common letter with x. For example, if "apple" has a common letter with "banana" (the letter 'a'), then "banana" also has a common letter with "apple".

Transitive Property:
- The relation R is not transitive because if x has a common letter with y, and y has a common letter with z, it does not necessarily mean that x has a common letter with z. For example, "apple" has a common letter with "banana" ('a'), and "banana" has a common letter with "cherry" ('a'), but "apple" does not have a common letter with "cherry".
Therefore, the relation R is reflexive, symmetric, and not transitive, making the correct answer option 'A'.
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Let W denote the words in the English dictionary. Define the relation R by R = {(x, y) ∈ W × W| the words x and y have at least one letter in common}. Then, R isa)reflexive, symmetric and not transitiveb)reflexive, symmetric and transitivec)reflexive, not symmetric and transitived)not reflexive and symmetricCorrect answer is option 'A'. Can you explain this answer?
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Let W denote the words in the English dictionary. Define the relation R by R = {(x, y) ∈ W × W| the words x and y have at least one letter in common}. Then, R isa)reflexive, symmetric and not transitiveb)reflexive, symmetric and transitivec)reflexive, not symmetric and transitived)not reflexive and symmetricCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let W denote the words in the English dictionary. Define the relation R by R = {(x, y) ∈ W × W| the words x and y have at least one letter in common}. Then, R isa)reflexive, symmetric and not transitiveb)reflexive, symmetric and transitivec)reflexive, not symmetric and transitived)not reflexive and symmetricCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let W denote the words in the English dictionary. Define the relation R by R = {(x, y) ∈ W × W| the words x and y have at least one letter in common}. Then, R isa)reflexive, symmetric and not transitiveb)reflexive, symmetric and transitivec)reflexive, not symmetric and transitived)not reflexive and symmetricCorrect answer is option 'A'. Can you explain this answer?.
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