Question

Are the following pairs of sets equal ? Give reasons.

(i) A = {2,3}, B = {x : x is a solution of $x^2+5x+6=0$}

(ii) A = {x : x is a letter of the word "WOLF"}

B = {x : x is a letter of the word "FOLLOW"}

Answer 1

(i) Two sets A and B are said to be equal if every elements of A is an elements of B and vice-versa.

We have, A = {2,3}

and B = {x : x is a solution of $x^2+5x+6=0$}

{$=x:x^2+3x+2x+6=0$}

{$=x:x(x+3)+2(x+3=0)$}

{$=x:(x+3)(x+2)=0$}

{$=x:x=-2,-3$}

{$=-2,-3$}

Hence $A\ne B$

(ii) A = {W, O, L, F}

B = {F, O,L, W}

[$beause$ repetition is not allowed]

= {W, O, L, F}

[The order in which the elments are written does not matter.] Hence A = B.