Five partners $($Upper P $1,$ Upper P $2,$ Upper P $3,$ Upper P $4,$ and Upper P $5)$ jointly own an electric company. Upper P $1$ owns $19$ shares of the$$ company, Upper P $2$ owns $14$shares$,$ Upper P $3$ and Upper P $4$ each own $13$shares$,$ and Upper P $5$ owns $6$shares$,$ with the usual agreement that one share equals one vote. Describe the partnership as a weighted voting system using the standard notation left bracket q: w $1$ comma w $2$ comma Bold $...$ comma w Subscript n Baseline right bracket under the following conditions.

$($a$)$ Decisions in the partnership are made by simple majority.

$($b$)$ Decisions in the partnership require two dash thirds of the votes.

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Part $1$

$($a$)$ The description of this voting system in standard notation is $[$

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Part $2$

$($b$)$ The description of this voting system in standard notation is $[$

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