Question

A transitive relation defined on ( 1,4,9) is

a. {(I, 1). (4,4). (9, 4)}

b. {(1,4).(4,1),(1, 1)}

c. {(1,4),(4,9). (9.9)}]

d. {(1,1),(1,4),(9,4),(4,1)}

e. {(1,4),(4,9),(1,9),(9,4)}​

Answer 1

Given :  relation defined on ( 1,4,9)

To Find : A transitive relation defined on ( 1,4,9) is

a. {(I, 1). (4,4). (9, 4)}

b. {(1,4).(4,1),(1, 1)}

c. {(1,4),(4,9). (9.9)}]

d. {(1,1),(1,4),(9,4),(4,1)}

e. {(1,4),(4,9),(1,9),(9,4)}​

Solution:

Transitive relation if for all a₁ , a₂ . a ₃∈ A    (a₁ , a₂) ∈ R   and   (a₂ , a₃ ) ∈ R  we get   (a₁ , a₃ ) ∈ R

संक्रामक  (transitive)   कहलाता है यदि  समस्त a₁ , a₂ . a ₃∈ A के   लिए (a₁ , a₂) ∈ R   तथा    (a₂ , a₃ ) ∈ R  से    (a₁ , a₃ ) ∈ R  प्राप्त हो

A transitive relation defined on ( 1,4,9)

( 1, 4)   ∈  ( 1,4,9)  

( 4, 9)   ∈  ( 1,4,9)  

=> ( 1, 9)   ∈  ( 1,4,9)  

( 1, 9)   ∈  ( 1,4,9)  

(9  , 4) ∈  ( 1,4,9)  

=> ( 1, 4 ) ∈  ( 1,4,9)  

{(1,4),(4,9),(1,9),(9,4)}​  is transitive relation defined on ( 1,4,9)

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