Discussion Forum : Relations And Functions Ii
Question -


Let R be a relation over the set N×n and it is defined by (a, b) R (c, d)   a+ d = b + c.  Then, R is

Options:
A .   reflexive only
B .   symmetric only
C .   transitive only
D .   an equivalence relation
Answer: Option D
:
D
(a, b) R (a, b) because a + b = b + a.  So, r is reflexive.
(a, b)R (c, d) a+d = b+c c+b = d+a
(c,d) R (a,b)
So, R is symmetric.
(a, b) R (c, d) and (c, d) R (e, f)
                   a + d = b + c, c + f = d + e
       Adding,         a + d + c + f = b + c + d +e
                  a + f = b + e
                      (a, b) R (e, f).
R is transitive.
 

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