Q3 of 58 Page 12

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.

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


To find: 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}


Hence,


x = 1, 21,………, 2p – 1, 2p – 1


So, Y = {1, 21,………, 2p – 1, 2p – 1}


More from this chapter

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1

Write the following sets in the roaster from

(i) A = {x : x ∈ R, 2x + 11 = 15}


(ii) B = {x | x2 = x, x ∈ R}


(iii) C = {x | x is a positive factor of a prime number p}

 2

Write the following sets in the roaster form:

(i)


(ii)


(iii)

4

State which of the following statements are true and which are false. Justify your answer.

(i) 35 ∈ {x | x has exactly four positive factors}.


(ii) 128 ∈ {y | the sum of all the positive factors of y is 2y}


(iii) 3 ∉ {x | x4 – 5x3 + 2x2 – 112x + 6 = 0}


(iv)496 ∉ {y | the sum of all the positive factors of y is 2y}.

 5

Given L = {1, 2, 3, 4}, M = {3, 4, 5, 6} and N = {1, 3, 5}

Verify that L – (M ∪ N) = (L – M) ∩ (L – N)