Question

Which of the following sets are equal ?

(i) A = {1, 2, 3}

(ii) B = {$xϵR:x^2-2x+1=0$}

(iii) C = {1, 2, 2, 3}

(iv) D = {$xϵR:x^3-6x^2+11x-6=0$}.

Answer 1

(i) A = {1, 2, 3}

(ii)B = {$xϵR:x^2-2x+1=0$} = { $xϵR:x=1,1$} = {1}

(iii) C = {1, 2, 3} ( $\because$ repetition is not allowed in a set)

(iv) D = {$xϵR:x^3-6x^2+11x-6=0$}.

= {$xϵR:(x-1)(x^2-5x+6)=0$}

[ $\because x=1$ satisfies the above equation]

= { $xϵR:(x-1)(x-2)(x-3)=0$}

= {$xϵR:x=1,2,3$ }

= {1, 2, 3}
Hence the set A, C and D are equal.