1.     Let R be the relation on the set A = {1, 2, 3, 4, 5, 6, 7} defined by the rule                (a b R, )Î if the integer (a – b) is divisible by 4. List the elements of R and its  inverse?
                                                                                                                                 
b)                 Check whether the relation R on the set S = {1, 2, 3} is an equivalent             relation where                                               
  = {(1,1), (2,2), (3,3), (2,1), (1,2), (2,3), (1,3), (3,1)}. Which of the  following properties R has: reflexive, symmetric, anti-symmetric,   transitive? Justify your answer in each case?                                
                           
c)                  Let = {,             ,             } and = {(, ),        (, ),        (, ),             (, ),         (, )}, find  [], []                                    
              and [] (that is the equivalent class of a, b, and c). Hence or otherwise find the             set of equivalent class of , and ?                                     ​