# 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
reshown Jul 6

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 by (31,090 points)
+1 vote
C is the answer answered Jul 7 by (770 points)
Can you provide the explanation?
what is refinement and congruence class?
refinement is defined in the question it self. a is congruent to b modulo 6 means |a-b| = 6k where k is integer.