Reference no: EM132380991
Relations Problems -
Problem 1 - List the elements of the relation ⊆ on the set ρ({a, b, c}).
Problem 2 - Give examples of relations that are (a) reflexive and symmetric but not transitive, (b) reflexive and anti-symmetric, (c) anti-symmetric, transitive, but not reflexive, and (d) reflexive, symmetric, and transitive. Do not use relations on numbers or sets.
Problem 3 - Complete the proof of Proposition 2.20, i.e., prove that if R is a partial order on X, then R- = R \ IdX is a strict order.
Problem 4 - Consider the less-than-or-equal-to relation ≤ on the set {1, 2, 3, 4} as a graph and draw the corresponding diagram.
Problem 5 - Show that the transitive closure of R is in fact transitive.
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