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Solution


Q.

Let A = {–2, –1, 0, 1, 2, 3}. Let R be a relation on A defined by xRy if and only if y = max{x, 1}. Let l be the number of elements in R. Let m and n be the minimum number of elements required to be added in R to make it reflexive and symmetric relations, respectively. Then l + m + n is equal to          [2025]
1 13  
2 12  
3 14  
4 11  

Ans.

(2)

We have, A = {–2, –1, 0, 1, 2, 3} and

R = {(–2, 1), (—1, 1), (0, 1), (1, 1), (2, 2), (3, 3)}.

Now, number of elements in R i.e., l = 6

For R to be reflexive,

R = {(–2, –2), (–1, –1), (0, 0), (–2, 1), (–1, 1), (0, 1), (1, 1), (2, 2), (3, 3)}

So, we need to add three elements to make it reflexive.

∴   m = 3

For R to be symmetric,

R = {(–2, 1), (1, –2), (–1, 1), (1, –1), (0, 1), (1, 0), (1, 1), (2, 2), (3, 3)}

So, we need to add three elements to make it symmetric.

∴   n = 3

So, l + m + n = 6 + 3 + 3 = 12.