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

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

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(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

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(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