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}

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

Solution of equation x² + 5x + 6 = 0

⇒ x² + 3x + 2x + 6 = 0

⇒ x(x + 3) + 2(x + 3) = 0

⇒ (x + 3)(x + 2) = 0

⇒ x = {-3,-2}

Let we represent the set B in roaster form:

⇒ Set B = {x is solution of x² + 5x + 6 = 0}={-3,-2}.

And set A ={2,3}

Two set A and B are said to be equal if they have exactly same elements then we say A = B.

Because the elements of set A and B do not have same numbers.

∴ A≠B.

(ii) Given: A = {x : x is a letter in the word FOLLOW},B = {y : y is a letter in the word WOLF}.

Let we represent the set A in roaster form:

⇒ Set A = {x : x is a letter in the word FOLLOW}={F,O,L,W}.

Let we represent the set B in roaster form:

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

Two set A and B are said to be equal if they have exactly same elements then we say A = B.

Because elements of set A and B do not have significant order, but A and B have same element.

∴ A=B.