Question

n(R'nS')+n(R'nS)=3,n(Rns)=4 and n(S'nR)=7,find n(U)

Answer 1

Answer:

3(RNs) this the rough answer

Answer 2

SOLUTION

GIVEN

n(R' ∩ S') + n(R' ∩ S) = 3 ,

n(R ∩ S) = 4 , n(S' ∩ R) = 7

TO DETERMINE

The value of n(U)

EVALUATION

Here it is given that

n(R' ∩ S') + n(R' ∩ S) = 3

n(R ∩ S) = 4 , n(S' ∩ R) = 7

Now n(R' ∩ S') + n(R' ∩ S) = 3

⇒ n((R ∪ S)') + n(S) - n(S ∩ R) = 3

⇒ n(U) - n(R ∪ S) + n(S) - n(S ∩ R) = 3

⇒n(U) - n(R) - n(S) + n(S∩R) + n(S) - n(S∩R) = 3

⇒ n(U) - n(R) = 3 - - - - - - (1)

Again n(S' ∩ R) = 7

⇒ n(R) - n(S ∩ R) = 7

⇒ n(R) - 4 = 7

⇒ n(R) = 11

From Equation 1 we get

n(U) - n(R) = 3

⇒ n(U) - 11 = 3

⇒ n(U) = 14

FINAL ANSWER

n(U) = 14

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