1.

Show that each of the relation R in the set A={x in Z: 0lt= xlt=12},given by R = {(a,b) : a=b} is an equivalence relation. Find the set of all elements related to 1 in each case.

Answer»

Solution :R={(1,1),(2,2),(3,3),(4,4),(5,5),(6,6),(7,7),(8,8),(9,9),(10,10),(11,11),(12,12)}
R is reflexive, symmetric and transitive.
`THEREFORE`R is equivalence relation.
Set of all ELEMENTS related to 1 is {1}.


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