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Let R be the relation on S = {1, 2, 3, 4, 5} defined by
R = {(1,3); (1, 1); (3, 1); (1, 2); (3, 3); (4, 4)}.
(b) Write down the matrix of R.
(c) Draw the digraph of R.
(d) Explain whether R is reáexive, irreáexive, symmetric, antisymmetric, transitive. Describe!
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prove same homotopy type is an equivalent relation
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