Teaching Sets for Grade 10

Teaching sets for grade 10

For SEE Question No.11

Key to remember

• If A and B are two disjoint subsets of universal set U then n(A∪B) = n(A)+n(B)
• If A and B are overlapping subsets of universal subsets of U then n(A∪B)= n(A)+n(B)-n(A∩B)
• If A, B and C  are overlapping subsets of universal subsets of U then n(A∪B∪C)= n(A)+n(B)+n(C)-n(A∩B)-n(B∩C)-n(A∩C)+n(A∩B∩C)
• n(AUB)'= n(U)-n(A∪B)
• n(A∪B∪C)'=n(U)- n(A∪B∪C)

Examples
1. In a group of 150 students, 120 like to play volleyball, 85 like to play football and 25 like none of the games[(150 जना मानिसको एक समुहमा 120 जनालाई भलीबल र 85 जनालाई फुटबल खेल्न मन पर्दो रहेछ | यदि 25 जनालाई कुनै पनि खेल खेल्न मन पर्दो रहेनछ भने]i) Show the above relation in Venn diagram [माथिको तथ्यांकलाई भेन चित्रमा देखाउनुहोस]ii) How many people like to play both the games? [कति जनालाई दुवै खेल खेल्न मन पर्दो रहेछ ?]iii) How many people like to play volleyball only? [कति जनालाई भलिबल मात्र खेल्न मन पर्दो रहेछ]

Solution:
Let V and F denotes the set of people who like to play volleyball and football respectively.

n(U)=150

n(V)=120

n(F)=85

n(VUF)'=25

n(V∩F)= ?

n_{0(V)= ?}

_{By using Venn diagram,}

n(U)=120-x+x+85-x+25
Or,150=230-x
Or, x=230-150
Or, x=80
∴ 80 people like both the games.
Number of people who like volleyball only = 120-x
                                                                      = 120-80
                                                                      = 40.

2.In a survey of community, it was found that 55% like summer season, 20% like winter season, 40% do not like both the seasons and 750 like both the seasons. By drawing Venn diagram, find the number of people who like winter season.

Solution:
Let S and D denote the set of people who like summer and winter season respectively.
n(U)= 100%
n(S)=  55%
n(D)= 20%
n(S∪D)=40%
n(S∩D)=?
let, n(S∩D) = x%
Then by using Venn diagram,
n(U) = 55%-x+x+20%-x+40%
Or,100% =115%-x
Or,x = 115%-100%
Or, x=15%
∴ 15% students like both the seasons.
Let, total no of students be y
then 15% of y=750
Or, 15y =75000
Or, y = 5000
Total number of people is 5000
Number of people who like winter season=20% of 5000=1000

3. In a survey of 400 students of a school, 210 liked Pokhara, 240 liked Kathmandu and 140 liked both the places then [400   जना विद्यार्थीहरु भएको एउटा विद्यालयमा सर्वेक्षण गर्दा 210 जनाले पोखरा मन पराए 240 जनाले काठमाडौँ मन पराए र 140  जनाले दुवै ठाउँ मन पराए भने] i)Show the above information in a Venn diagram[ माथिको तथ्य लाई भेन चित्रमा देखाउनुहोस] ii)Find the number of students who liked neither of the places.[दुवै ठाउँ मन नपराउने विद्यार्थी संख्या पत्त्ता लगउनुहोस् | 

Solution:

Let P and K denotes the set of students who like Pokhara and Kathmandu respectively.

n(U) = 400

n(P) = 210

n(K) = 240

n(P∩K) = 140

n(P∪K)' = ?

Let, n(P∪K)' = x

Then using Venn diagram 

n(U) = 70+100+140+x

Or, 400 = 310+x

Or, x=400-310

Or, 90

ஃ 90 students liked neither of the places.

4.In a survey of 120 students it was found that the ratio of students who liked Mathematics and Science is 4:5. Out of which 10 students liked both the subjects 20 like none of them.[120 जना विद्यार्थीहरुमा गरिएको सर्वेक्षणमा गणित र विज्ञान मन पराउने  विद्यार्थीहरुको अनुपात 4:5 पाईयो जसमध्ये  10 जनाले दुवै विषय  मन पराउने र 20 जनाले कुनै पनि विषय मन नपराउने पाईयो भने]i) Draw a Venn diagram to show the above information.[माथिको तथ्यलाई भेन चित्रमा देखाउनुहोस् ] ii) Find the number of students who like Mathematics only.[ गणित मात्र मन पराउनेको संख्या पत्त्ता लगाउनुहोस् ]

Solution:
Let M and S denote the set of students who liked Mathematics and Science respectively.
n(U) =120

let, n(M)= 4x

n(S) = 5x
n(M∩S)= 10
n(MUS)' = 20

n_{0(M) =?}

_{By using Venn diagram,}

n(U)=4x-10+10+5x-10+20
Or,120 = 9x +30
Or, 9x=120-30
Or, 9x=90
Or, x=10
ஃ Number of students who liked Mathematics only = 4x-10 = 4×10-10= 40-10=30

5. In an examination of 200 students, 70 passed in Accounts, 80 in  English, and 60 in Computer, 35 passed in Accounts and English, 25 passed in English and computer, 30 passed in Accounts and Computer and 15 passed in all three subjects.

• Show the above information in Venn diagram
• How many students could not pass in all three subjects?

Solution: Left for an exercise.

Do you need classroom videos? Click the link below.

1. Domain and range part one

2. Properties of determinant part- 1

3. Properties determinants part-2