# Write the following sets in the roaster form:

Question:

Write the following sets in the roaster form:

(i) $D=\left\{t \mid t^{3}=t, t \in R\right\}$

(ii) $E=\left\{w \mid \frac{w-2}{w+3}=3, w \in \mathbf{R}\right\}$

(iii) $\mathrm{F}=\left\{\mathrm{x} \mid \mathrm{x}^{4}-5 \mathrm{x}^{2}+6=0, \mathrm{x} \in \mathbf{R}\right\}$

Solution:

(i) According to the question,

D = {t | t3 = t, t ∈ R}

Roster form,

t3 = t

⇒ t3 – t = 0

⇒ t(t2 – 1) = 0

⇒ t(t – 1)(t + 1) = 0

⇒ t = 0, -1 or 1

Hence, D = {-1, 0, 1}

(ii) According to the question,

$E=\left\{w \mid \frac{w-2}{w+3}=3, w \in R\right\}$

Roster form,

((W – 2)/(W + 3))=3

⇒ w – 2 = 3(w + 3)

⇒ w – 2 = 3w + 9

⇒ 3w – w = – 9 – 2

⇒ 2w = –11

⇒ w = –11/2

Hence, E = {– 11/2}

(iii) According to the question,

F = {x | x4 – 5x2 + 6 = 0, x ∈ R}

Roster form,

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

⇒ x = ±√3 or ±√2

⇒ x = √3, –√3, √2 or –√2

Hence, F = {–√3, –√2, √2, √3}