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