Consider the following Hasse diagram of a partially ordered setRP, , where},,,,{ 54321 xxxxxP . Find the least and greatest members inP if they exist. Also findthe maximal and minimal elements ofP . Find the upper and lower bounds of2 3 4{ , , }x x x,},,{ 542 xxx and},,{ 321 xxx . Also indicate the LUB and GLB of these subsetsif they exist.

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

ssignment TwoOpen course indexBackQuestion 1Not yet answeredMarked out of 1.00Flag questionTipsQuestion textLet a set S = {2, 4, 8, 16, 32} and ≤≤ be the partial order defined by S≤≤R if a divides b. Number of edges in the Hasse diagram of is ______Question 1Answer5469Clear my choicePrevious activityAssignment OneJump to...Next activityAssignment ThreeContact us Follow us Contact site supportYou are logged in as KARWERU JOHN NJENGA # (Log out)Data retention summaryGet the mobile appGet the mobile appThis theme was developed by

Let pP, ĺ1q and pQ, ĺ2q be two posets. Their product poset is defined as the product set P ˆQ, togetherwith a partial order relation ĺ, where we say that:pp1, q1q ĺ pp2, q2q if and only if p1 ĺ1 p2 and q1 ĺ2 q2.For the purposes of this problem, let P and Q be the divisor posets of 8 and 9 respectively, with thestandard (divisibility) order relations in each case. That is, P consists of all the divisors of 8 and Qof all the divisors of 9.(a) How many elements does the product poset P ˆ Q have? Justify briefly.(b) Draw the Hasse diagram of P ˆ Q, labelling each node.

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

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.