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Sets and Binary Relations

2. Let A be the set { 1,2,3,4,5,6} and R be a binary relation on A defined as :

{(1,1), (1,3), (1,5), (2,2), (2,6), (3,1), (3,3), (3,5), (4,4), (5,1), (5,3), (5,5), (6,2), (6,6)}

(a) Show that R is reflexive.
(b) Show that R is symmetric.
(c)Show that R is transitive.

3. Let A be the set {1,2,3,4,5,6} and let F be the class of subsets of A defined by:

[{1,6}, {2,3,5}, {4}]

(a) Show that F is a partition of A.
(b) Find the equivalence on A determined by F.
(c) Draw the directed graph of the equivalence relation found in part (2).

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