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Home » If Y = {x | x is a positive factor of the number 2p – 1 (2p – 1), where 2p – 1 is a prime number}. Write Y in the roaster form.
If Y = {x | x is a positive factor of the number 2p – 1 (2p – 1), where 2p – 1 is a prime number}. Write Y in the roaster form.
CBSE | Class 11 | Maths | NCERT Exemplar | Sets
If Y = {x | x is a positive factor of the number 2p – 1 (2p – 1), where 2p – 1 is a prime number}. Write Y in the roaster form.

Solution:

As per the question,

Y=\left\{x \mid x\right. is a positive factor of the number 2^{p-1}\left(2^{p}-1\right), in which 2^{p}-1 is a prime number \}.

Roster form,

1 and p itself are the only possible positive factors of a prime number p.

The possible factors of 2^{p-1}\left(2^{p}-1\right) are all possible factors of 2^{p-1} and 2^{p}-1 individually.

The possible factors of 2^{p-1} are 2^{0}, 2^{1} \ldots 2^{p-1} and that of 2^{p}-1 are 1 and 2^{p}-1\left\{\because ~{{2}^{p}}~\text{-}1\text{ }is\text{ }prime\text{ }number\}

Hence,

x=1,2^{1} \ldots 2^{p-1}, 2^{p}-1

As a result, Y=\left\{1,2^{1} \ldots 2^{p-1}, 2^{p}-1\right\}

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