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}