Q1.prove that n(A union B)=n(A) +n(B)-n (A intersection B). 'A' is the set of prime numbers less than 10. 'B' is the set of odd numbers less than 10
Answers
Step-by-step explanation:
SOLUTION
GIVEN
- 'A' is the set of prime numbers less than 10.
- 'B' is the set of odd numbers less than 10
TO PROVE
n(A ∪ B) = n(A) + n(B) - n (A ∩ B)
EVALUATION
Here it is given that
A' is the set of prime numbers less than 10.
∴ A = { 2 , 3 , 5 , 7 }
So n(A) = 4
'B' is the set of odd numbers less than 10
∴ B = { 1 , 3 , 5 , 7 , 9 }
So n(B) = 5
Again
A ∪ B = { 1 , 2 , 3 , 5 , 7 , 9 }
So n(A ∪ B) = 6
Also A ∩ B = { 3 , 5 , 7 }
So n(A∩B) = 3
We have to verify
n(A ∪ B) = n(A) + n(B) - n (A ∩ B)
LHS = n(A ∪ B) = 6
RHS = n(A) + n(B) - n (A ∩ B) = 4 + 5 - 3 = 6
Hence LHS = RHS
Hence verified
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