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Solution


Q.

Let A={1, 2, 3, 4, 5}. Let R be a relation on A defined by xRy if and only if 4x≤5y. Let m be the number of elements in R and n be the minimum number of elements from A×A that are required to be added to R to make it a symmetric relation. Then m+n is equal to:            [2024]
1 24  
2 26  
3 25  
4 23  

Ans.

(3)

   Given, A={1,2,3,4,5}

   R={(x,y):4x≤5y, x,y∈A}

   R={(1,1),(1,2),(1,3),(1,4),(1,5),(2,2),(2,3),(2,4),(2,5),(3,3),(3,4),(3,5),(4,4),(4,5),(5,4),(5,5)}

   ∴  n(R)=16=m

   Elements needed to make R symmetric={(2,1),(3,1),(4,1),(5,1),(3,2),(4,2),(5,2),(4,3),(5,3)}  i.e., 9 elements

   ∴  n=9

   So, m+n=16+9=25