Q. 5
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}
Answers
Answer:
(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.