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

JEE Main Mathematics question

Let denote the words in the English dictionary. Define the relation by the words and have at least one letter in common. Then, is

(A)Reflexive, symmetric and not transitiveCorrect
(B)Reflexive, symmetric and transitive
(C)Reflexive, not symmetric and transitive
(D)Not reflexive, symmetric and transitive

Answer: (A)

Solution

Reflexive: every word shares all of its letters with itself, so is true. Symmetric: if and have a common letter, then and have that same common letter. Transitive:

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Question ID VK-007329