# DM-Sets,Relations and Functions-Q13

+1 vote

A partition P1 is called a refinement of the partition P2 if every set in P1 is a subset of one of the sets in P2.

S1: The partition of the set of bit strings of length 16 formed by equivalence classes of bit strings that agree on the last eight bits is a refinement of the partition formed from the equivalence classes of bit strings that agree on the last four bits

S2: The partition formed from congruence classes modulo 6 is a refinement of the partition formed from congruence classes modulo 3

Which of the following statements is true?

(A). Only S1
(B). Only S2
(C). Both S1 and S2
(D). None of the above asked Jul 5, 2019
reshown Jul 6, 2019

First, try to understand what is refinement.

A partition P1 is called a refinement of the partition P2 if every set in P1 is a subset of one of the sets in P2.

S1: The partition of the set of bit strings of length 16 formed by equivalence classes of bit strings that agree on the last eight bits is a refinement of the partition formed from the equivalence classes of bit strings that agree on the last four bits

Here in P1  for each distinct pattern of last 8 bits one partition is created.  In P2 for each distinct pattern of last 4 bits one partition is created.
Every partition of P1 is a subset of some partition of P2, so P1 is refinement of P2.
In same way in S2 too P1 is refinement of P2. answered Jul 9, 2019 by (34,850 points)
+1 vote