Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 2 - Set Theory - 2.4 Set Operations and Venn Diagrams with Three Sets - Exercise Set 2.4 - Page 95: 116



Work Step by Step

In the provided Venn diagram, it contains eight region representing the eight common blood groups. There are three antigens A, B, and Rh. So the blood with Rh antigen is labeled positive and lacking Rh antigen is labeled negative. According to this information, the required sets are: \[\begin{align} & U=\left\{ {{\text{A}}^{+}},{{\text{A}}^{-}},A{{B}^{+}},A{{B}^{-}},{{B}^{+}},{{B}^{-}},{{O}^{+}},{{O}^{-}} \right\} \\ & A=\left\{ {{\text{A}}^{+}}\text{,}{{\text{A}}^{-}}\text{,A}{{\text{B}}^{+}}\text{,A}{{\text{B}}^{-}} \right\} \\ & B=\left\{ \text{A}{{\text{B}}^{+}}\text{,A}{{\text{B}}^{-}}\text{,}{{\text{B}}^{+}}\text{,}{{\text{B}}^{-}} \right\} \\ & C=\left\{ {{\text{A}}^{+}}\text{,A}{{\text{B}}^{+}}\text{,}{{\text{B}}^{+}}\text{,}{{\text{O}}^{+}} \right\} \end{align}\] So, in the innermost region V, the blood group \[\text{A}{{\text{B}}^{+}}\]indicating that the person having that blood group type has antigens A, B and Rh. Blood type O(both positive and negative) lacks antigens A and B. Type \[{{\text{O}}^{+}}\]has antigen Rh only. But blood type \[{{\text{O}}^{-}}\] lacks all three antigens A, B, and Rh. “In the blood transfusion, the recipient must have all or more of the antigens present in the donor’s blood”. In the Venn diagram, blood group \[{{\text{A}}^{-}}\]is in the region I so it contains only antigen A. And the person whose blood group\[{{\text{A}}^{+}}\]is in the region IV, so it has antigens A and Rh. Here, the person with \[{{\text{A}}^{+}}\]blood type is a receiver and \[{{\text{A}}^{-}}\]blood type is a donor. Clearly, receiver has all and in fact, more antigens than the donor’s blood. Therefore, it can receive blood from the person of\[{{\text{A}}^{-}}\] blood type. So, \[{{\text{A}}^{-}}\]person can donate blood to a \[{{\text{A}}^{+}}\]person.
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