Below is a Venn diagram involving two sets A and B, in which the cardinalities are given as below \(n_o(A)=p\) \(n_o(B)=q\) \(n(A \cap B)=r\) \(n ( \overline{A \cup B})=s\)
Out of 100 students in a school, 60 passed in english, 70 in mathematics, 5 failed in both subjects and 10 did not appear in the examination.
एक विद्यालयका 100 जना विद्यार्थीमध्ये अंग्रेजीमा 60 जना उतीर्ण, गणितमा 70 जना उतीर्ण, र दुवै विषयमा 5 जना अनुत्तीर्ण भए र 10 जना परीक्षामा सहभागी भएनन् ।
Write set notation of cardinality of students who passed in both subjects.
दुवै विषयमा उत्तीर्ण विद्यार्थीहरूको संख्या समुह संकेतमा लेख्नुहोस् ।[1]
Present above information in a Venn-diagram. माथिको जानकारी भेन-चित्रमा प्रस्तुत गर्नुहोस् ।[1]
Find the number of students who passed in both subjects. दुवै विषयमा उत्तीर्ण भएका विद्यार्थीहरूको सङ्ख्या पत्ता लगाउनुहोस् ।[3]
Find the ratio of passeed and failed students in both subjects. दुवै विषयमा उत्तीर्ण र अनुत्तीर्ण विद्यार्थीको अनुपात पत्ता लगाउनुहोस् ।[1]
Write set notation of cardinality of students who passed in both subjects
दुवै विषयमा उत्तीर्ण विद्यार्थीहरूको संख्या समुह संकेतमा लेख्नुहोस् ।
Let U=Set all students E= Set of students who passes in english M= Set of students who passes in mathematics
Now, according to the question
Set notation of students who passed in both subjects english and mathematics is \(n(E \cap M)\)
Present above information in a Venn-diagram माथिको जानकारी भेन-चित्रमा प्रस्तुत गर्नुहोस् ।
Say, \(n(E \cap M)=x\)
Then, the Venn-diagram is given below.
Find the number of students who passed in both subjects दुवै विषयमा उत्तीर्ण भएका विद्यार्थीहरूको सङ्ख्या पत्ता लगाउनुहोस् ।
According to the question
Given that \(n(U)= 100\) \(n(E)= 60\) \(n(M)= 70\) \(n(\overline{E \cup M})= 5+10=15\) \(n(E \cap M)=x\)
According to venn-diagram \(100=(60-x)+x+(70-x)+ 15\)
or\(x=45\)
So, number of students who passed in both subjects is \(n(E \cap M)=x=45\)
Find the ratio of passed and failed students in both subjects दुवै विषयमा उत्तीर्ण र अनुत्तीर्ण विद्यार्थीको अनुपात पत्ता लगाउनुहोस् ।
We found Number of students who passed in both subjects is \(n(E \cap M)=45\) Number of students who failed in both subjects is \(n(\overline{E \cup M})=15\) So, the Ratio of student is \(\frac{n(E \cap M)}{n(\overline{E \cup M})}=\frac{45}{15}=3:1 \)
Write set notation of cardinality of students who passed in both subjects
दुवै विषयमा उत्तीर्ण विद्यार्थीहरूको संख्या समुह संकेतमा लेख्नुहोस् ।
मानौ U= सम्पुर्ण बिद्यार्थीहरुको समुह E=अंग्रेजी बिषयमा पास हुने बिद्यार्थीहरुको समुह M= गणित बिषयमा पास हुने बिद्यार्थीहरुको समुह
अब, प्रश्नानुसार
अंग्रेजी र गणित दुबै बिषयमा पास हुने बिद्यार्थीहरुको संख्यालाई समुह संकेतमा निम्नानुसार जनाईन्छ । \(n(E \cap M)\)
Present above information in a Venn-diagram माथिको जानकारी भेन-चित्रमा प्रस्तुत गर्नुहोस् ।
मानौ, \(n(E \cap M)=x\)
अब, माथिको जानकारीलाई भेन-चित्रमा तलका अनुसार प्रस्तुत गर्न सकिन्छ।
Find the number of students who passed in both subjects दुवै विषयमा उत्तीर्ण भएका विद्यार्थीहरूको सङ्ख्या पत्ता लगाउनुहोस् ।
प्रश्नानानुसार
दिएको \(n(U)= 100\) \(n(E)= 60\) \(n(M)= 70\) \(n(\overline{E \cup M})= 5+10=15\) \(n(E \cap M)=x\)
भेन चित्र अनुसार \(100=(60-x)+x+(70-x)+ 15\)
or\(x=45\)
यहाँ, दुवै विषयमा उत्तीर्ण भएका विद्यार्थीहरूको सङ्ख्या \(n(E \cap M)=x=45\) हो ।
Find the ratio of passed and failed students in both subjects दुवै विषयमा उत्तीर्ण र अनुत्तीर्ण विद्यार्थीको अनुपात पत्ता लगाउनुहोस् ।
मथिको उत्तर अनुसार दुवै विषयमा उत्तीर्ण हुने विद्यार्थीको सङ्ख्या \(n(E \cap M)=45\) दुवै विषयमा अनुत्तीर्ण हुने विद्यार्थीको सङ्ख्या \(n(\overline{E \cup M})=15\)
त्यसैले, दुवै विषयमा उत्तीर्ण र अनुत्तीर्ण विद्यार्थीको अनुपात \(\frac{n(E \cap M)}{n(\overline{E \cup M})}=\frac{45}{15}=3:1 \) हो ।
Question
100 जना मानिसहरूको समूहमा गरिएको सर्वेक्षणमा 50 जनाले आइफोन र 60 जनाले एन्ड्रोइडफोन मन पराएको पाइयो र 20 जनाले यी दुई फोनहरू मन पराएको पाइयो ।
In a survey of 100 people, it was found that 50 people liked I-phone and 60 people like Android phone, and 20 people like both of these phones.
आइफोन र एन्ड्रोइड दुबै फोन मन नपराउने मानिसहरूको गणनात्मकता समुह संकेतमा लेख्नुहोस ।
Write the cardinality notation of people who like both of these phones.
[1]
माथिको जानकारीलाई भेनचित्रमा प्रस्तुत गर्नुहोस्।
Present the above information in a Venn-diagram.
[1]
आइफोन र एन्ड्रोइड दुबै फोन मन नपराउने मानिसहरूक संख्या पत्ता लगाउनुहोस्।
Find the number of people who does not like both of these phones. [3]
आइफोन र एन्ड्रोइड फोन कुनै एउटा मात्र मन पराउनेको संख्या तुलना गर्नुहोस्।
Compare the number of people who like only one of these two phones.
[1]
Solution
Let U is universal set of all survayed people
Given that I is set of people who like I-phone A is set of people who like Android phone
Thus
Cardinality of all surveyed people as Universal Set U is \(n(U)=100\)
Cardinality of set I, people who liked I-phone is \(n(I)=50\)
Cardinality of set A, people who liked Android phone is \(n(A)=60\)
Cardinality of set, people who lie both of these two phones is \(n (I \cap A)=20\)
Now the itemwise solution are :
Write the cardinality notation of people who like both of these phones.
According the question, \(n (I \cap A)=20\)
Present the above information in a Venn-diagram.
According the question,
Let us suppose that \(n (\overline{I \cup A})=x\)
Then, the Venn-diagram of given information are as follows.
Find the number of people who does not like both of these phones.
According to the Venn-diagram given above \((50-20)+(20)+(60-20)+(x)=100\)
or\(x=10\)
Therefore,
The number of people who does not like both of these phones is \(n (\overline{I \cup A})=10\)
Compare the number of people who like only one of these two phones.
According to the solution
The number of people who like I-phone only is \(n_o(I)=50-20=30\)
The number of people who like Android phone only is \(n_o(A)=60-20=40\)
It shows that
Number of people who like I-phone only and Android phone only is in the ration of 3:4
No comments:
Post a Comment