Mathematics, 09.04.2021 15:40 dannisundrop
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 ?
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1. Let R be the relation on the set A = {1, 2, 3, 4, 5, 6, 7} defined by the rule
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