Verify that (a+b=b+a) where a=11/4 and b=3/5
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Class 11
>>Applied Mathematics
>>Set theory
>>Applications of set theory in real life
>>If ξ = {natural numbers between 10 and
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If ξ={ natural numbers between 10 and 40}
A={ multiples of 5} and B={ multiples of 6}, then
(i) find A∪B and A∩B
(ii) verify that n(A∪B)=n(A)+n(B)−n(A∩B)
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Solution
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From the question it is given that, ξ={ natural numbers between 10 and 40}
ξ={11,12,13,14,15,…,39}
ξ is a universal set and A and B are subsets of ξ Then, the elements of A and B are to be taken only from ξ
A={ multiples of 5}
A={15,20,25,30,35}
B={ multiples of 6}
B={12,18,24,30,36}
(i) A∪B={15,20,25,30,35,40}∪{12,18,24,30,36}
A∪B={15,20,25,30,35,12,18,24,36}
A∩B={30}
(ii) n(A∪B)=n(A)+n(B)−n(A∩B)
n(A∪B)=5
n(A)=5
n(B)=5
n(A∩B)=1
Then, n(A)+n(B)−n(A∩B)=5+5−1=9
By comparing the results, 9=9
Therefore, n(A∪B)=n(A)+n(B)−n(A∩B)
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a + b is 11/4 + 3/5 = 67/20; b + a is 3/5 + 11/4 = 67/20
Hence, a + b = b + a = 67/20