We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
35
0
avatar

This is question about partial ordered sets and function.

 

Let ⟨A,≼A⟩ be a poset, B a set, and f : B → A a function. Let ≼B ⊆ B × B be the relation defined by, for all x,y ∈ B, x ≼B y if and only if f(x) ≼A f(y).

(a) Show that if ≼B is a partial order then f is injective.

(b) Show that if f is injective then ≼B is a partial order.

 Nov 8, 2019

25 Online Users

avatar
avatar