n the following, state whether A = B or not:

Question

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 ...} 

Answer 1

(i) A = {a, b, c, d}; B = {d, c, b, a} The order in which the elements of a set are listed is not significant. ∴ A = B 

(ii) A = {4, 8, 12, 16}; B = {8, 4, 16, 18} It can be seen that 12 ∈ A but 12 ∉ B. ∴ A ≠ B 

(iii) A = {2, 4, 6, 8, 10} B = {x: x is a positive even integer and x ≤ 10} = {2, 4, 6, 8, 10} ∴ A = B 

(iv) A = {x: x is a multiple of 10} B = {10, 15, 20, 25, 30 …} It can be seen that 15 ∈ B but 15 ∉ A. ∴ A ≠ B