SOLUTION: Let A = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 4), (2, 1), (2, 2), (3, 3), (4, 1), (4, 4)} be a binary relation on A. Then (a) Decide whether the given relation R is reflexiv

Question 367564: Let A = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 4), (2, 1), (2, 2), (3, 3), (4, 1), (4, 4)}
be a binary relation on A. Then
(a) Decide whether the given relation R is reflexive, irreflexive, symmetric, and/or transitive. Justify with reasons.
(b) Draw the directed graph of R.
(c) Write matrix representation of the given relation R on set A

Answer by Jk22(389) (Show Source): You can put this solution on YOUR website!
R = {(1, 1), (1, 2), (1, 4), (2, 1), (2, 2), (3, 3), (4, 1), (4, 4)}

a) reflexive since for all element i, i<->i, i is in relation with itself
(1,1), (2,2), (3,3), (4,4)

symmetric, since if (a,b) exists, (b,a) exists too (1,2), (2,1); (1,4), (4,1)

transitive, since the cases are trivial : (1,2)(2,2), (2,1)(1,1), (1,4)(4,4)

b)

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