Answer:
(a) A∪B = {-12,-5,-3, 0, 1, 4, 6, 17}
(b) A∩B = {1,4}
(c) A∩C = {-3,1,17}
(d) A ∪ (B ∩ C) = {-5,-3,0,1,4,17}
(e) A ∩ B ∩ C = {1}
(f) A ∪ C, the set is infinite.
(g) (A ∪ B) ∩ C = {-5,-3,1,17}
(h) A ∪ (C ∩ D), the set is infinite.
Step-by-step explanation:
(a) Recall that the union of A and B is the set that contains all the elements that are in A or in B, and that in set notation no repetitions are allowed, so we can only write 1 once.
(b) Recall the the intersection of A and B is the set formed by the elements that are in A and B at the same time. In this case, only 1 and 4 satisfy that condition.
(c) In this case we list only the elements in A that are odd.
(d) In this case we perform first the operation B ∩ C={-5}. Then, we perform A∪{-5}.
(e) Recall that set operations are associative, so A ∩ B ∩ C = (A ∩ B )∩ C. As we have calculated A∩B = {1,4}, we only need to find the odd numbers, which is only 1.
(f) The set is infinite because C is infinite. Recall that the union of an infinite set with any other, is infinite too. In plain words, when we perform a union of set we are adding elements.
(g) These are the elements that are in A ∪ B and are odd too.
(h) Notice that the set C ∩ D is infinite, because is formed by the positive odd integers. So, its union with any other set is infinite too.
