Which of the following collections of subsets of S={1,2,3,4,5,6} form a partitio

Question

Which of the following collections of subsets of S={1,2,3,4,5,6} form a partition S? If the given collection of sets does form a partition, then list the ordered pairs if the equivalence relation produced by the partition. If the given collection does not form a partition, then explain which part(s) of the definition of partition fails.
a. {1,3},{5,4},{2,6}
b. {1,2,3,}, {3,4}, {5,6}
c. {1}, {2}, {5}, {4,3,6}
d. {1,3,4}, {2,6}

Explanation / Answer

Partition of a set follows two properties: union of all its entities is the whole set intersection of any two entities is empty. a) is a partition (both the properties are satisfied) b) {1,2,3} ,{3,4} have 3 in common -> not a partition c) satisfies both => partition d) partition -> both properties satisfied

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