Question

Determine the partitions of the set {3, 4, 5, 6, 7} from the following subsets.

(a) {3,5}, {3,6,7}, {4,5,6}

(b) {3}, {4,6}, {5}, {7}

(c) {3,4,6}, {7}

(d) {5,6}, {5,7}

The question was posed to me in an interview for job.

My query is from Relations topic in chapter Relations of Discrete Mathematics

Answer 1

Right option is (b) {3}, {4,6}, {5}, {7}

To explain I would say: {3,5}, {3,6,7}, {4,5,6}. It is not a partition because these sets are not pairwise disjoint. The elements 3, 5 and 6 appear repeatedly these sets. {1}, {2,3,6}, {4}, {5} – this is a partition as they are pairwise disjoint. {3,4,6}, {7} – this is not a partition as element 5 is missing.

{5,6}, {5,7} – this is not a partition because it is missing the elements 3, 4 in any of the sets.