Question

Its urgent
pls give this Answer



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Answer 1

Answer:

u and p are algebraic letters used to denote

Answer 2

Given :

U = {1, 2, 3, 7, 8, 9, 10, 11, 12}

P = {1, 3, 7, 10}

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To do :

• Find the value P'.
• Show the sets U, P and P' by Venn diagram.
• Verify (P')' = P

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Solution :

$\sf\color{black}{\star}$ Finding P' -

We are given U and P and we need to calculate P'.

Therefore ,

⠀⠀⠀⠀⠀$\bf\:P'=\big\{x|x∈U~and~x ∉ P\big\}$

Simply,⠀⠀⠀⠀

⠀⠀⠀⠀⠀$\bf\:P'=U-P$

$\sf\to\:P'=\big\{1,2,3,7,8,9,10,11,12\big\}-\big\{1,3,7,10\big\}$

$\sf\to$ $\small\blue{\tt\pmb{P'=\big\{2,8,9,11,12\big\}}}$

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$\sf\color{black}{\star}$ Venn Diagram -

⠀⠀⠀⠀⠀Refer to the attachment.

$\small\blue{\tt\pmb{\multimap}}$ The number inside circle denotes the elements of P.

$\small\blue{\tt\pmb{\multimap}}$ The number inside square denotes the elements of P'.

$\small\blue{\tt\pmb{\multimap}}$ Finally when we consider both P and P' i.e., elements inside circle and square we get Venn diagram for U.

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$\sf\color{black}{\star}$ Verifying (P')' = P -

For verifying let's first calculate the value of (P')'

Now,

⠀⠀⠀$\bf\:(P')'=\big\{x|x∈U~and~x ∉ P'\big\}$

Simply,

⠀⠀⠀$\bf\:(P')'=U-P'$

And we do know that,

⠀⠀⠀ P' = {2,8,9,11,12}

Therefore,

$\sf\to\:(P')'=\big\{1,2,3,7,8,9,10,11,12\big\}-\big\{2,8,9,11,12\big\}$

$\sf\to\:(P')'=\big\{1,3,7,10\big\}$

⠀⠀⠀⠀⠀

Finally, now we have both the values of (P')' and P , so let's verify :

$\sf\:(P')'=P$

Substituting the values

$\sf\to\big\{1,3,7,10\big\}=\big\{1,3,7,10\big\}$

$\small\blue{\tt\pmb{Hence~Verified!~}}$

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Note :

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