Textbook Examples:

1. In a high school graduation class, (x,y) is in the relation r if person x is the same height as person y. Is this reflexive?
   
   Yes, (x,x) will always be the same, as person x is always the height of person x.
2. In a high school graduation class, (x,y) is in the relation r if person x is the same age as y. Is this symmetrical?
   
   Yes. If you are the same age as someone else, then they are the same age as you.
3. In a high school graduation class, (x,y) is in the relation r if person x is the same height as person y. Is this transitive?
   
   Yes. If (x,y) are in the relation, then the height of x = the height of y. If (y,z) is in the relation, that means that the height of y = the height of z. So, the height of z = the height of x, so it is transitive.

Practice Problems (Try these on your own):

What properties does the equation X ≤ Y have...

1. If x = 3?
2. If x = 3 and y = 4?
3. If x = 3 and y = 4 and z = 5?