Solutions to Chapter 35 Properties of relations

A. Give examples of relations with the following properties:

1. 1.
   ​

   Reflexive but not symmetric blank _x is no older than blank _y

2. 2.
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   Symmetric but not transitive blank _x is within 1 km of blank _y

3. 3.
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   Transitive, symmetric, but not reflexive blank _x is a full (i.e., not half) sibling of blank _y

B. Show that a relation can be both symmetric and anti-symmetric by giving an interpretation that makes both of the following sentences true:

domain:

$0$

$R(x,y)$:

$⟨$$0$, $0$$⟩$