Exercise 5. Show by example that P may be a strict partial order (so,by the previous result, the two definitions of R coincide) but R not aweak order.

Q1. Consider the relation R on the set of integers as xRy if and only if x<y. Then prove that R is partial order relation.

Define Partial Order relation and check whether R is Partial Order relation.R= {(x,y) 𝑖𝑓 𝑦 = 𝑥𝑟, 𝑟 𝑖𝑠 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑎𝑛𝑑 𝑎, 𝑏 ∈ 𝑍}

Assume the R is a relation on a set A, aRb is partially ordered such that a and b

Consider the relation R on P dened by:R = (x; y) | y = 2^i * x for some i 2 N:(a) Prove that R is a partial order on N.(b) Identify the minimal elements of R.(c) Let A = {1; 2; 3; 5; 6; 12}. Draw the Hasse diagram for the poset dened by this relation

Assume the R is a relation on a set A, aRb is partially ordered such that a and b are _____________ans.reflexive and transitivetransitivereflexivesymmetric Previous Marked for Review Next