ECE 108 Post Midterm

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Last updated 11:14 PM on 7/1/26
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10 Terms

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Relation

Subset that defines relations between elements between A and B

R is a subset of A x B

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Thm #1

If R is a non=empty relation, R cannot be both reflexive and irreflexive

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If R is a subset of A², Then R is Asymmetric if and only if R is antisymmetric and irreflexive

Proof with Antisymmetric First

<p>Proof with Antisymmetric First</p>
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Proof going the other direction

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Simplification

When you destroy information, you drop the associativity symbol

<p>When you destroy information, you drop the associativity symbol</p>
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Rules #1

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Rules #2

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Example of Transitivity

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Equivalence Relation

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When doing these proofs, assume the first part (the IF statement part is true) then prove the second part (After the “THEN” statement)

<p>When doing these proofs, assume the first part (the IF statement part is true) then prove the second part (After the “THEN” statement)</p>