Questions
Let R be a relation over the set and it is defined by Then R is
a
Reflexive only
b
Symmetric only
c
Transitive only
d
An equivalence relation
detailed solution
Correct option is D
We have a, bR(a, b) for all (a, b)∈N×NSince a+b=b+a. Hence, R is reflexive.R is symmetric for we have (a, b)R(c, d)⇒a+d=b+c⇒d+a=c+b⇒c+b=d+a⇒(c,d)R(e,f).Then by definition of R, we havea+d=b+c and c+f=d+e,whence by addition, we geta+d+c+f=b+c+d+e or a+f=b+eHence, (a,b)R(e,f)Thus, (a, b)R(c, d) and (c, d)R(e,f)⇒(a, b)R(e, f).Talk to our academic expert!
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