Theory question 102
Sets(a) If a is the set {1, 2, 3, ……, 19, 20} and A, B and C are subsets of a such that A = {multiples of five}, B = {multiples of four}, C = {multiples of three}, list the elements of (i) A (ii) B (iii) C
(b) Find; (i) A∩B (ii) A∩C (iii) B∪C
(c) Using your results in (b) show that (A∩B) ∪ (A∩C) = A∩(B∪C).
Show the model answer
Model answer
(a)(i) A = {5, 10, 15, 20} (ii) B = {4, 8, 12, 16, 20} (iii) C = {3, 6, 9, 12, 15, 18}.
(b)(i) A∩B = {20} (ii) A∩C = {15} (iii) B∪C = {3, 4, 6, 8, 9, 12, 15, 16, 18, 20}.
(c) (A∩B) ∪ (A∩C) = {20} ∪ {15} = {15, 20}.
A∩(B∪C): the elements of A that are in B∪C are 15 and 20, so A∩(B∪C) = {15, 20}. The two sets are equal.
Explanation
Work out both sides separately and show they contain the same elements.