Question

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

option:-
{3,5}, {3,6,7}, {4,5,6}

{3}, {4,6}, {5}, {7}

{3,4,6}, {7}

{5,6}, {5,7}​

Answer 1

Given :  set {3, 4, 5, 6, 7}

To Find : Determine the partitions of the set from given options

{3,5}, {3,6,7}, {4,5,6}

{3}, {4,6}, {5}, {7}

{3,4,6}, {7}

{5,6}, {5,7}​

Solution:

partitions of the set is a set of non empty subsets  and each element is a part of one subset only

Also all elements  are part of one of the subset

{3,5}, {3,6,7}, {4,5,6}

Here element 3  , 5 and  6 are in more than  one subset hence this is not

partition  set

{3}, {4,6}, {5}, {7}    All elements 3 ,4  ,5 , 6 , 7  are used.  No element is in more than one subset  , there is no empty subset

Hence This is partition  set  of  {3, 4, 5, 6, 7}

{3,4,6}, {7}   element 5 is not part of any subset hence this is not

partition  set

{5,6}, {5,7}​  5 is  in more than  one subset also 3 and 4 are part of any subset  hence this is not  Partition  set

From the given option : {3}, {4,6}, {5}, {7}   is partition set of {3, 4, 5, 6, 7}

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Determine the partitions of the set {3, 4, 5, 6, 7 }

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