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

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Basic Math

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 appearsearlier in this problem set. Unless told otherwise, you may use anyof 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, notantireflexive, and not transitive. You must use set-list notationfor your answer.

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

(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.

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