MathematicsThe relation SS defined on the set of real numbers by the rule aSb , if a⩾b is an:

The relation SS defined on the set of real numbers by the rule aSb , if ab is an:


  1. A
    An equivalence relation
  2. B
    Reflexive, transitive but not symmetric
  3. C
    Symmetric, transitive but not reflexive
  4. D
    Neither transitive nor reflexive but symmetric  

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    Solution:

    Let a be any real number,
    Then we can always write a≥a. that is, aSa .
    Thus, relation S is a reflexive relation over set R.
     Let a,b,c be three real numbers such that, aSb and bSc,
    aSb implies a≥b and bSc implies b≥c.
    So, we can definitely write, a≥c and thus aSc.
    So, Relation S is transitive.
     Let a,b be any two real numbers such that aSb,
    aSb implies a≥b,but we can't necessarily write b≥a
    So, Relation S is not symmetric.
    Reflexive, transitive but not symmetric.
    Hence, option 2 is correct.
      
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