Are the following pair of sets equal? Give reasons.

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
(i) A = {2, 3}; B = {x: x is a solution of x² + 5x + 6 = 0}
Factorize the equation
x² + 5x + 6 = 0
x² + 3x + 2x + 6 =0
x(x + 3) + 2(x + 3) = 0
(x + 2)(x + 3) = 0
x = -2 or x = -3
-2 and -3 are not equal to element of set A which is 2, 3.
Hence, A ≠ B

(ii) A = {x: x is a letter in the word FOLLOW}
FOLLOW and WOLF both have letter W, O, L and F.
Hence, A = B.