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: 115

Answer

No

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 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 IV so it contains antigen A and Rh but not B. So, the person whose blood group is \[{{\text{A}}^{+}}\] can donate blood to \[{{\text{A}}^{+}}\]and\[\text{A}{{\text{B}}^{+}}\]blood types but cannot donate to a person whose blood type is\[{{\text{A}}^{-}}\], since blood type \[{{\text{A}}^{-}}\] is in the region I so it has only one antigen A. Therefore, it cannot receive blood from the person of\[{{\text{A}}^{+}}\] blood type.
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