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99 Percentile Qs Bank for JEE MainMathematicsSets and Relations

If R be a relation from A = 1 , 2 , 3 , 4 to B = 1 , 3 , 5 such that a , b ∈ R ⇔ a < b , then R O R - 1 is

Options

  1. A( 1 , 3 ) , ( 1 , 5 ) , ( 2 , 3 ) , ( 2 , 5 ) , ( 3 , 5 ) , ( 4 , 5 )
  2. B( 3 , 1 ) , ( 5 , 1 ) , ( 3 , 2 ) , ( 5 , 2 ) , ( 5 , 3 ) , ( 5 , 4 )
  3. C( 3 , 3 ) , ( 3 , 5 ) , ( 5 , 3 ) , ( 5 , 5 )
  4. D( 3 , 3 ) , ( 3 , 4 ) , ( 4 , 5 )

Correct answer

C. ( 3 , 3 ) , ( 3 , 5 ) , ( 5 , 3 ) , ( 5 , 5 )

Step-by-step solution

A = 1 , 2 , 3 , 4 and B = 1 , 3 , 5 ∴ R = ( 1 , 3 ) , ( 1 , 5 ) , ( 2 , 3 ) , ( 2 , 5 ) , ( 3 , 5 ) , ( 4 , 5 ) and R - 1 = ( 3 , 1 ) , ( 5 , 1 ) , ( 3 , 2 ) , ( 5 , 2 ) , ( 5 , 3 ) , ( 5 , 4 ) Now, 3 → R - 1 1 → R 3 ⇒ 3 , 3 ∈ R O R - 1 5 → R - 1 1 → R 5 ⇒ 5 , 5 ∈ R O R - 1 5 → R - 1 2 → R 3 ⇒ 5 , 3 ∈ R O R - 1 3 → R - 1 1 → R 5 ⇒ 3 , 5 ∈ R O R - 1 ∴ R O R - 1 = 3 , 3 , 3 , 5 , 5 , 3 , 5 , 5

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