#### Question

Eight blood types are shown by the eight regions of the Venn diagram shown here. Each circle represents one of three antigens: A, B or Rh. If A and B are both absent, the blood type is O. If Rh is present, the blood type is positive (+); otherwise, it is negative (-). The following table represents the blood types of 150 people.

Antigens | Number of people |

A | 60 |

B | 27 |

Rh | 123 |

A and B | 12 |

A and Rh | 46 |

B and Rh | 17 |

A and B and Rh | 9 |

- A,B र Rh ले क्रमश: A, B र Rh एन्टीजेनलाई जनाउँछ भने सबै समुहलाई गणनात्मकता सङ्केतमा लेख्नुहोस् ।

If A,B and Rh denote the set of people who have A, B र Rh Antigens in their blood respectively, write the cardinality notation of people for all groups.[1K]
- मााथिको जानकारीलाई भेनचित्रमा प्रस्तुत गर्नुहोस् ।

Show the above information in a Venn diagram. [1U]
- कति जना मानिसहरुमा ओ नेगेटिभ रगत समुह रहेछन् ? गणना गर्नुहोस् ।

How many people are having O negative blood? Calculate it. [3A]
- रगत प्राप्त गर्दा, प्राप्तकर्तासँग दाताको सबै एन्टिजेनहरू हुनुपर्छ। अब, ओ पोजेटिभ भएको व्यक्तीले कति जना मानिसलाई रगत दान गर्न सक्दछ?

When receiving a blood, the recipient must have all the antigens of the donor. If a person has O positive, to how many people he can donate the blood?[1HA]

Solution 👉 Click Here

Solution
Let

U is universal set of all antigens
Given that

A denote the set of people having A antigens
B denote the set of people having B antigens
Rh denote the set of people having Rh antigens
Thus

Cardinality of all surveyed people as Universal Set U is

\(n(U)=150\)
Now the itemwise solution are :

- If A,B and Rh denote the set of people who have A, B र Rh Antigens in their blood respectively, write the cardinality notation of people for all blood groups.

According the question,

Cardinality of set, people having A, B and Rh antigens is

\(n(A \cap B \cap Rh )=n(AB+)=9\)

Cardinality of set, people having A and Rh antigens only is

\(n_o(A \cap Rh )=n(A+)=46-9=37\)

Cardinality of set, people having B and Rh antigens only is

\(n_o(B \cap Rh )=n(B+)=17-9=8\)

Cardinality of set, people having A and B antigens only is

\(n_o(A \cap B )=n(AB-)=12-9=3\)

Cardinality of set A, people having A antigens only is

\(n_o(A)=n(A-)=60-37-9-3=11\)

Cardinality of set B, people having B antigens only is

\(n_o(B)=n(B-)=27-8-9-3=7\)

Cardinality of set Rh, people having Rh antigens only is

\(n_o(Rh)=n(O+)=123-37-9-8=69\)

- Present the above information in a Venn-diagram.

According the question,

The Venn-diagram of given information are as follows.
- How many people are having O negative blood? Calculate it.

According to the Venn-diagram given above

\(n(U)=150\)

or\(69+11+7+37+3+8+9+x=150\)

or\(x=6\)

Therefore,

The number of people having O negative blood is

\(n \overline{(A \cup B \cup Rh)}=6\)

- When receiving a blood, the recipient must have all the antigens of the donor. If a person has O+, to how many people he can donate the blood?

According to the solution

A person having O+ blood, can donate blood to

people having Rh antigens

people having O+,A+,B+, AB+ blood groups

Which is

\(n(Rh)=123\)

Thus, A person having O+ blood, can donate blood to 123 people

This completes the solution

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