#SETTHEORY

Question

Q) Suppose A={a,b,c,d} and Π1 is the following partition of A

Π1={{a,b,c}{d}}

And let Π2={{a},{b},{C},{d}} Π3={{a,b,c,d}} and Π4={{a,b},{c,d}},
Draw a Poset diagram of the poset, ⟨{Π1,Π2,Π3,Π4},refines ⟩.

What does refines means here ?

Comments

A refines B iff every partition/Block of A is subset of some partition of B.Using this you can draw hasse diagram

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https://gateoverflow.in/1725/gate1998-11

Answer 1

For Complete Details of “Refinement of a Partition” with ALL possible variations, GATE questions, and also Applications in Theory of Computation,

Watch the following lecture:

Refinement of a Partition - Complete Details & Analysis

For this question, detailed video solution is below:

Detailed Video Solution of GATE CSE 2007 Question 26 Refinement of a Partition

Suppose we have two partitions of a set $S : P_1 = \left \{ A_1,A_2,A_3... \right \} , \,and\,\, P_2 = \left \{ B_1,B_2,B_3... \right \}$

We say that $P_1$ is a refinement of $P_2$ if every $A_i$ is a subset of some $B_j$ . Or We can say that $P_1$ refines $P_2$