Question

Are the following pair of sets equal? Give reasons.

(i) A = {2, 3}; B = {x: x is solution of x² + 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 x² + 5x + 6 = 0}

The equation x² + 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

(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