Question

Define A = {x : 0 ≤ x ≤ 1}, B = {x : 0 ≤ x ≤ 3}, and C = {x : −1 ≤ x ≤ 2}. Draw diagrams showing each of the following sets of points: (a) AC ∩ B ∩C (b) AC ∪(B ∩C) (c) A ∩ B ∩CC (d) [(A ∪ B)∩CC ] C

Answer 1

Answer: (a) {0,1}; (b) {0,1, 2}; (c) {0,1}; (d) {0, 1, 2}

Step-by-step explanation: Defining the sets A,B and C:

A = {0,1};  B = {0, 1, 2, 3}; C = {-1, 0, 1, 2}

(a) A ∩ B ∩ C = {0, 1}, because it represents the intersection of the sets, the items that appears in all the three sets.

(b) A ∪ (B ∩ C) = {0, 1} ∪ {0, 1, 2} = {0, 1, 2}. In this case, it represents the union of the sets A with the intersection of sets B and C.

The (c) and (d) are a combination between union and intersection of the sets.

The Venn Diagrams are the representations of the sets and their interactions and are represented in the attachments