DM-Sets,Relations and Functions-Q13

Question

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

Answer 1

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. 

Answer 2

C is the answer

Comments

Can you provide the explanation?

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what is refinement and congruence class?

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refinement is defined in the question it self. a is congruent to b modulo 6 means |a-b| = 6k where k is integer.