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If Y = {x | x is a positive factor of the number 2p – 1 (2p – 1),

Question:

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:

According to the question,

Y = {x | x is a positive factor of the number 2p – 1(2p – 1), where 2p – 1 is a prime number}.

Roster form of given set,

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

Possible factors of 2p – 1 (2p – 1) are all possible factors of 2p – 1 and 2p – 1 individually.

Possible factors of 2p – 1 are 20, 21… 2p – 1 and that of 2p – 1 are 1 and 2p – 1 {∵ 2p – 1 is prime number}

Therefore,

x = 1, 21… 2p – 1, 2p – 1

Hence, Y = {1, 21… 2p – 1, 2p – 1}

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