define the sets a, b, c, and d as follows:

a = {-3, 0, 1, 4, 17}
b = {-12, -5, 1, 4, 6}
c = {x ∈ z: x is odd}
d = {x ∈ z: x is positive}
for each of the following set expressions, if the corresponding set is finite, express the set using roster notation. otherwise, indicate that the set is infinite.

(a)

a ∪ b

(b)

a ∩ b

(c)

a ∩ c

(d)

a ∪ (b ∩ c)

(e)

a ∩ b ∩ c

(f)

a ∪ c

(g)

(a ∪ b) ∩ c

(h)

a ∪ (c ∩ d)

(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.

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step-by-step explanation: