Solution to List the members of the equivalence relation on (1, 2, 3, 4) defined by the … - Sikademy
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Archangel Macsika

List the members of the equivalence relation on (1, 2, 3, 4) defined by the following partition. Find the equivalence classes [1], [2], [3] and [4] 1. {(1, 2), (3, 4)) 2. {{1, 2, 3), (4)) 3. {{1}, {2}, {3}, {4}}

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Let us list the members of the equivalence relation R on X=\{1, 2, 3, 4\} defined by the following partition P . Find the equivalence classes [1], [2], [3] and [4].


It is well-known that (a,b)\in R if and only if a,b\in M for some M\in P. The equivalence class generated by a is [a]=\{x\in X:(a,x)\in R\}.


1. \{\{1, 2\}, \{3, 4\}\}


It follows that R=\{(1,1),(1,2),(2,1),(2,2),(3,3),(3,4),(4,3),(4,4)\}.

[1]=\{1,2\}=[2],\ \ [3]=\{3,4\}=[4].


2. \{\{1, 2, 3\}, \{4\}\}


It follows that R=\{(1,1),(1,2),(2,1),(2,2),(3,3),(1,3),(3,1),(2,3),(3,2),(4,4)\}.

[1]=\{1,2,3\}=[2]=[3],\ \ [4]=\{4\}.


3. \{\{1\}, \{2\}, \{3\}, \{4\}\}


It follows that R=\{(1,1),(2,2),(3,3),(4,4)\}.

[1]=\{1\},\ \ [2]=\{2\},\ \ [3]=\{3\},\ \ [4]=\{4\}.


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Question ID: mtid-5-stid-8-sqid-1450-qpid-1188