Q2 of 58 Page 12

Write the following sets in the roaster form:

(i)


(ii)


(iii)

(i) Given: D = {t | t3 = t, t ∈ R}


To find: Roster form of given set


t3 = t


⇒ t3 – t = 0


⇒ t(t2 – 1) = 0


⇒ t(t – 1)(t + 1) = 0


⇒ t = 0, -1 or 1


So, D = {-1, 0, 1}


(ii) Given:


To find: Roster form of given set



⇒ w – 2 = 3(w + 3)


⇒ w – 2 = 3w + 9


⇒ 3w – w = - 9 – 2


⇒ 2w = –11




(iii) Given: F = {x | x4 – 5x2 + 6 = 0, x ∈ R}


To find: Roster form of given set


x4 – 5x2 + 6 = 0


⇒ x4 – 3x2 – 2x2 + 6 = 0


⇒ x2(x2 – 3) – 2(x2 – 3) = 0


⇒ (x2 – 3) (x2 – 2) = 0


⇒ x2 = 3 or 2





More from this chapter

All 58 →
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}

 3

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.

 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)