Proposition 8.1.1.1.4 (01RA): Properties of Reflexive Relations

Preferences





Font:

PDF Style:

Here's a breakdown of the differences between each PDF style:

Style	Class	Font	Theorem Environments
Style 1	`book`	Alegreya Sans	`tcbthm`
Style 2	`book`	Alegreya Sans	`amsthm`
Style 3	`book`	Arno*	`amsthm`
Style 4	`book`	Computer Modern	`amsthm`

*To be replaced with Linus Romer's Elemaints when it is released.

Let $R$ and $S$ be relations on $A$.

Interaction With Inverses. If $R$ is reflexive, then so is $R^{\dagger }$.
Interaction With Composition. If $R$ and $S$ are reflexive, then so is $S\mathbin {\diamond }R$.

Proof of Proposition 8.1.1.1.4.

Item 1: Interaction With Inverses

Clear.

Item 2: Interaction With Composition

Clear.

Noticed something off, or have any comments? Feel free to reach out!

You can also use the contact form below: