In the following, state whether A = B or not:
(i) A = {a, b, c, d} B = {d, c, b, a}
(ii) A = {4, 8, 12, 16} B = {8, 4, 16, 18}
(iii) A = {2, 4, 6, 8, 10} B = {x : x is positive even integer and x ≤ 10}.
(iv) A = {x : x is a multiple of 10}, B = {10, 15, 20, 25, 30, . . .}
(i) Given: A = {a, b, c, d} B = {d, c, b, a}.
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.
(ii) Given: A = {4, 8, 12, 16} B = {8, 4, 16, 18}.
Two set A and B are said to be equal if they have exactly same elements then we say A = B.
As 12 Є A but 12 does not belongs to B.
Because elements of set A and B do not have same element.
∴ A≠B.
(iii) Given: A = {2, 4, 6, 8, 10} B = {x : x is positive even integer and x ≤ 10}.
Let we represent the set B in roaster form:
⇒ x is positive even integer and x ≤ 10= {2,4,6,8,10}.
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 have same element.
∴ A=B.
(iv) Given: A = {x : x is a multiple of 10}, B = {10, 15, 20, 25, 30, . . .}
Let we represent the set A in roaster form:
⇒ Set A = x is a multiple of 10= {10, 20 , 30 ,…}.
And set B ={10, 15, 20, 25, 30, . . .}
Two set A and B are said to be equal if they have exactly same elements then we say A = B.
As 15 Є B but 15 does not belongs to B
Because elements of set A and B do not have same element.
∴ A≠B.