In the class, we have discussed in details $[$sic$]$ Greedy for coverage maximization Problem on Boston, and the total resulting cost.

$3\mathrm{.}1)$ Consider such an instance as follows:

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n$=6,$

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m$=6$ and

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k$=2.$ Given the ground set is

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G$=\{1,2,...,6\}$ the collection of subset is

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in

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C$=\{$S

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$$i in $[$n$]\}$ with

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$=\{1,2,3\},$

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$=\{2,3,4\},$

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$=\{2,3,5\},$

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$=\{1,3,6\}$ please $[$sic$]$ subset output by Greedy and the corresponding coverage $(1)$ The collection of subset $[$sic$]$ sorted and the related coverage, and the sensitivity approximation ratio of Greedy on the specific instance.

$3\mathrm{.}2)$ Can you create another instance of max$-$cover such that the approximation ratio achieved by greedy on the instance is strictly less than that what $[$sic$]$ is shown above $($i$.$e$.,$ on the instance given in $3\mathrm{.}1)?$ Please state clearly your instance and detailed analysis to support your claim.