Question

Are the following pairs of sets equal? Give reasons.

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

(ii) A = {x : x is a letter in the word FOLLOW}

B = { y : y is a letter in the word WOLF}

Answer 1

(i) A = {2, 3} and

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

Now $x^2+5x+6=0$

$\Rightarrow x^2+3x+2x+6=0$

$\Rightarrow (x+3)(x+2)=0\Rightarrow x=-3,-2$

$\therefore B=\{-2,-3\}$

Hence A and B are not equal sets.

(ii) A = {x : x is a letter in the word FOLLOW}

= {F, O, L, W}

B = {y : y is a letter in the word WOLF} = {W, O, L, F}

Hence A = B = {F, O, L, W}