Are These Relations Reflexive, Antisymmetric, and Transitive?

[brookey86]

Homework Statement

Are these two relations reflexive, antisymmetric, transitive?

1. (w,x)<=(y,z) iff w+x <= y+z

2. (w,x)<=(y,z) iff w+x <= y+z AND w<y

Homework Equations

The Attempt at a Solution

1. reflexive - yes; antisymmetric - no; transitive - yes;

2. reflexive - yes; antisymmetric - yes; transitive - yes;

 

[lanedance]

would you say the second is reflexive?

 

[brookey86]

would you say the second is reflexive?

With the way I wrote it no. But I actually made a typo, it should be w+x <= y+z AND w<=y. So I'd say yes

 

[lanedance]

ok, would that change anything else?

 

[brookey86]

ok, would that change anything else?

No, I think #2 would still be antisymmetric and transitive