Let A be a set with $\lvert A \rvert$ = $4$. What is the max number of elements tht a relation R on A can contain so tht $R \cap R^{-1}$ = $\emptyset$

Asked May 01 '16 at 23:11

Active May 01 '16 at 23:20

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Let A be a set with $\lvert A \rvert$ = $4$. What is the maximum number of elements that a relation R on A can contain so that $R \cap R^{-1}$ = $\emptyset$?

I am not sure at all how to start this and my instructor says that it does not require a formal proof.

asked May 01 '16 at 23:11

Matt

Technically, everything requires a formal proof. In practice, this is a simple problem and one you can reason through very easily, since there are 16 ordered 2-tuples on a set with 4 elements, and it's very easy to figure out what to put in $R$ and $R^{-1}$ via guess-and-check. – Pockets May 01 '16 at 23:16

Let A be a set with $\lvert A \rvert$ = $4$. What is the max number of elements tht a relation R on A can contain so tht $R \cap R^{-1}$ = $\emptyset$

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