Question

Are the following pair of sets equal? Give reasons.
(i) A = {2, 3}; 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}; B = {x: x is a solution of $x^2+ 5x + 6 = 0$}
The equation $x^2+ 5x + 6 = 0$ can be solved as:
$x(x + 3) + 2(x + 3) = 0 (x + 2)(x + 3) = 0$
$x = -2$ or $x = -3$
∴ A = {2, 3}; B = {-2, -3}
∴ $A ≠ B$

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(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}
The order in which the elements of a set are listed is not significant.
A = B