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NTA Abhyas JEE Main2020MathematicsSets and RelationsPractice

Let W denotes the words in the English dictionary. If the relation R is given by R = x , y ∈ W × W : the word x a n d y h a v e a t l e a s t o n e l e t t e r i n c o m m o n , then R is

Options

  1. Areflexive, symmetric and not transitive
  2. Breflexive, symmetric and transitive
  3. Creflexive, not symmetric and transitive
  4. Dnot reflexive, symmetric and transitive

Correct answer

A. reflexive, symmetric and not transitive

Step-by-step solution

Given, R = ( x , y ) ∈ W × W : the word x and y have atleast one letter in common Let, W = cat , toy , you , … Clearly, R is reflexive and symmetric but not transitive. [Since, cat R toy , toy R you ⇏ cat R you ]

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