Question

let a and b be two sets such that n(A)=35 , n(A∩B)=11 and n(A∪B)'=17. if n(U)= 57 find
(1) n(B)
(2) n(A-B)
(3) n(B-A)

Answer 1

Answer:

n(B) = 16, n(A-B) = 24, N(B-A) = 5.

Step-by-step explanation:

Since n(U) = 57 and n(AUB)' = 17

Thus, n(AUB)= n(U) - n(AUB)'.

so, n(AUB)= 40 = n(A) + n(B) - n(A∩B)

i.e. n(B) = 16.

n(A-B) = n(A) - n(A∩B) = 24.

n(B-A) = n(B) - n(A∩B) = 5.

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Answer 2

Answer:

(1) n(B) = 16

(2) n(A-B) = 24

(3) n(B-A) = 5

Step-by-step explanation:

We have given that,

n(U) = 57

n(U) is the total number of elements in universal sets

n(A) = 35

n(A) is the total number of elements in set A

n(A∩B) = 11

n(A∩B) is the total number of elements common in set A and set B

n(A∪ B)' = 17

n(A∪ B)' total number of elements excluding the total number of elements in set A and set B

Now, we have to find n(B), n(A-B), and n(B-A)

Step 1

We have to find the total number of elements in set A and B, therefore,

n(A∪B) = n(U) - n(AUB)'

n(A∪B) = 57 - 17

n(A∪B) = 40

Now,

n(A∪B) = n(A) + (B)n - (A∩B)

40 = 35+ n(B) - 11

n(B) = 40+11-35

n(B) = 16

Step 2

We have to find n(A-B)

n(A-B) means elements from only set A excluding elements common between set A and B. Therefore,

n(A-B) = n(A) - n(A∩B)

n(A-B) = 35 - 11

n(A-B) = 24

Step 3

Now we have tofind n(B-A)

n(B-A) means elements from only set B excluding elements common between set A and B. Therefore,

n(B-A) = n(B) - n(A∩B)

n(B-A) = 16 - 11

n(B-A) = 5

Therefore,

n(B) = 16

n(A-B) = 24

n(B-A) = 5