2. Let A and B be two sets and U be their Universal set. If n(U)= 120, n(A)= 42, n(B)= 50 and n(AꓵB)= 21 then find, (i) n (AUB), n(A – B), n(B – A) and n(AˊꓵBˊ) (ii) n(Bˊ), n(Aˊ), n(AꓴB)ˊ (iii) n(PUQ) and n(PꓵQ) where P= A – B and Q= AꓵB (iv) How many elements are there in the set U – (AUB) - Advance Math Class 10- Exercise: 1.1

Let A and B be two sets and U be their Universal set. If n(U)= 120, n(A)= 42, n(B)= 50 and n(AꓵB)= 21 then find,  

(i) n (AUB), n(A – B), n(B – A) and n(AˊꓵBˊ)  

(ii) n(Bˊ), n(Aˊ),  n(AꓴB)ˊ  

(iii) n(PUQ) and n(PꓵQ) where P= A – B and Q= AꓵB  (iv) How many elements are there in the set U – (AUB)

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Solution:

Given,

n(A)= 42

n(B)= 50

n(AꓵB)= 21

i) We know that

n (AUB)= n(A) + n(B) – n(AꓵB)
              =42+50 – 21
              =71

Again, 

n (A ̶ B)= n(A)  ̶  n(AꓵB)
             = 42 – 21
             = 21

n (B ̶ A)= n(B)  ̶  n(AꓵB)
             = 50 – 21
             = 29

And 

n(AˊꓵBˊ)= n(AꓴB)ˊ
                = n(U) – n(AUB)
                = 120 – 71
                = 49

(ii) n(Bˊ) = n(U) – n(B)
                = 120 – 50
                = 70

n (Aˊ)= n(U) – n(A)
          = 120 – 42
          = 78

And 

n(AUB)ˊ= n(U) – n(AUB)
              = 120 – 71
              = 49

(iii) n(PUQ)= n [(A  ̶   B) U (AꓵB)]
                   = n[(AꓵBˊ) U (AꓵB)]
                   = n[Aꓵ(BˊUB)] (distribution law)
                   = n [AꓵU]
                   = n(A)
                   = 42

And 

n(PꓵQ)= n [(A  ̶  B) ꓵ (AꓵB)]
            = n[(AꓵBˊ) ꓵ (AꓵB)]
            = n[ A ꓵ (BꓵBˊ)]
            = n [A ꓵ ф]
            = n(ф)
            = 0

(iv) n[U – (AUB)] = n(U) – n(AUB)
                              = 120 – 71
                              = 49

  Exercise: 1.1  

1. For the set A= { x : x Є N and x < 10} and ф, find the followings

2. Let A and B be two sets and U be their Universal set. If n(U)= 120, n(A)= 42, n(B)= 50 and n(AꓵB)= 21 then find

3. If n(AꓵB)= 36, n(A – B)= 25, n(B – A)= 20, Then find n(AUB), n(A) and n(B).

5. In a class test in mathematics and English, it was found that 55 students have passed in Mathematics, 46 have passed in English and 35 passed in both the subjects. If the number of students who appeared in the test is 100, the find

6. In a survey of 550 students in a school, it was found that 175 students drink milk, 300 students drink tea and 110 students drink both milk and tea. Find the number of students who drinks neither milk nor tea.

7. In a survey among a group of employees of a central Govt. office in Assam, it was found that 80 of them can speak the Assamese, 70 of them can speak English and 50 of them can speak both Assamese and English. If each of the employees who took part in the survey can speak either Assamese or English or both of the two languages, then find

8. In a club of 250 members, it is found that 130 of them drink tea and 85 of them drink tea but not coffee. If each of the members of the club drinks at least one of the items between tea and coffee, the find-

9. In a class of 90 students, 60 students play volleyball, 53 students play badminton and 35 students play both of the games. Find the number of students

10. In a survey among 1500 families of a town it was found that 1263 families have TV, 639 families have radio and 197 families have neither TV nor Radio.

11. Out of 180 students of a class, 76 of them study Mathematics, 81 of them study Physics and 80 of them study Chemistry. Also, 34 of them study Mathematics and Physics, 30 of them study Mathematics and Chemistry and 33 of them study Physics and Chemistry. If 18 students study all the three subjects then find