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  • Write the following sets in the roaster form: (i) D = {t : t^2 = t, t in R} (ii) E = {w : w -2/w+3 = 3, w in R} (ii) F = {x : x^4 - 5x^2 + 6 = 0, x in R}

Write the following sets in the roaster form:

  1. D = \left\{t : t^3 = t, t\in R \right \}
  2. E = \left\{w:\frac{w-2}{w+3} = 3, w\in R \right \}
  3. F= \left\{x:x^4 -5x^2 + 6= 0, x\in R \right \}

Answers (1)

(i)    Given that D = \left\{t : t^3 = t, t\in R \right \}

        \begin{aligned}t^3 &= t \\ t^3 - t &= 0 \\ t(t-1)(t+1)&= 0 \\ t &= -1,0,1\end{aligned}

        hence, D = \left\{-1,0,1 \right \}

(ii)    Given that E = \left\{w:\frac{w-2}{w+3} = 3, w\in R \right \}

        \begin{aligned}\frac{w-2}{w+3} &= 3\\ 3w + 9 &= w-2 \\ 2w &= -11 \\ w& = -\frac{11}{2} \end{aligned}

        Hence, E = \left\{\frac{-11}{2} \right \}

(iii)    Given that F= \left\{x:x^4 -5x^2 + 6= 0, x\in R \right \}

        \begin{aligned} x^4 - 5x^2 + 6 &= 0 \\ (x^2-2)(x^2-3)&=0\end{aligned}

        x = \pm\sqrt2 and x = \pm\sqrt3

        Hence, F = \left\{-\sqrt{2}, + \sqrt{2}, -\sqrt{3}, + \sqrt{3}\right\}

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