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JEE MainMathematicsSets and Relations

Let X = 1, 2, 3, 4 and P(X) be the power set of X . A relation R is defined on P(X) such that for any two subsets A and B of X , A , R , B if and only if A B or B A . Then the relation R is :

Options

  1. Aan equivalence relation
  2. Bsymmetric and transitive only
  3. Creflexive and symmetric only
  4. Dreflexive only

Correct answer

C. reflexive and symmetric only

Step-by-step solution

For reflexivity: For any set A P(X) , we know that A A . Thus, the condition A A or A A is satisfied, which means A , R , A . So, R is reflexive. For symmetry: If A , R , B , then A B or B A . This logically implies B A or A B , which means B , R , A . So, R is symmetric. For transitivity: Let A = 1 , B = 1, 2 , and C = 2 . Here, A B , so A , R , B holds. Also, C B , which means B , R , C holds. However, neither A C nor C A is true, so A is not related to C . So, R is not transitive. Therefore, the relation R is re

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