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  • Write the following sets in the roaster form first D equals bracket t mod t to the power 3 equals t comma t belongs to R bracket second E equals bracket w mod w minus 2 by w plus 3 equals 3 comma w belongs to R bracket

Write the following sets in the roaster form:

(i) D = \left \{ t | t^{3} = t,t\epsilon R\right \}

(ii) E = \left \{ w |\frac{w-2}{w+3} =3 ,w\epsilon R\right \}

(iii) F = \left \{ x | x^{4} - 5x^{2} +6 =0 ,x\epsilon R\right \}

Answers (1)

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

t^{3} = t

t\left ( t^{2}-1 \right ) = 0

t\left ( t-1 \right )\left ( t+1 \right ) = 0

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

\frac{w-2}{w+3} =3

3w +9 = w-2

2w=-11

w=-\frac{11}{2}

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

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

x^{4} - 5x^{2} +6 =0

\left ( x^{2} -2 \right ) \left ( x^{2}-3 \right ) = 0

x^{2} -2 =0 , x^{2}-3 = 0

x = \pm \sqrt{2} , and , x=\pm \sqrt{3}

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

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