In Mathematics Textbook for Class XII of N.C.E.R.T 2006 edition, question no. 8 Exercise 1.1 reads as:
Show that the relation R in the set A = {1,2,3,4,5} given by
R = {(a,b) : Ia-bIis even} is an equivalence relation. Show that all the elements of {1,3,5} are related to each other and all the elements of {2,4} are related to each other. But no element of {1,3,5} is related to any element of {2,4}.
My doubt is:
Can we say that "the relation R in the set A = {1,2,3,4,5} given by
R = {(a,b) : Ia-bIis even} is an equivalence relation"?
In fact this will be true if relation R is reflexive. That is if a R a for all a belonging to A.
Which means that 1 - 1 = 0 is even.
Can we say ' 0 is even'?
Please comment.
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