Give an example of a relation that ﬁts the given requirements. If you think that there...

Give an example of a relation that ﬁts the given requirements. If you think that there is no such relation, you must explain why. In each case, you may not use any of the relations that appears earlier in this problem set. Unless told otherwise, you may use any of the following ways of deﬁning a relation: set-list notation, set-builder notation, or a directed graph.

(a) A relation on {a,b,c,d} that is not reﬂexive, not antireﬂexive, and not transitive. You must use set-list notation for your answer.

(b) A relation on {a,b,c,d} that is not symmetric and not anti-symmetric. You must use a directed graph to deﬁne this relation.

(c) A relation on the set of all text strings that is symmetric, but not transitive. You must use set-builder notation.

Please write each step neatly and nicely.

Expert Solution

milcah answered 2 years ago

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