Grade 12th passAlgebra
Sir please explain me question no 1,2 & 4...........
Sir please explain me question no 1,2 & 4...........
1 Answer
Anish Singhal
Approved Tutor Answer8 Years agoB denotes those who like apples. Let the population of America be 100, then
n(A)=63andn(B)=76
Now, n(A∪B)=n(A)+n(B)−n(A∩B)
N(A∪B)=63+76−n(A∩B)
N(A∩B)=139−n(A∪B)
But n(A∪B)≤100
So, 139−n(A∪B)≥139−100
139−n(A∪B)≥39
n(A∩B)≥39…………(i)
Now,n(A∩B)≤n(A)andn(A∩B)≤n(B)
n(A∩B)≤63andn(A∩B)≤76
n(A∩B)≤63……………(ii)
From Eqs. (i) and (ii),
39≤n(A∩B)≤63
39≤x≤63
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n(A)=63andn(B)=76
Now, n(A∪B)=n(A)+n(B)−n(A∩B)
N(A∪B)=63+76−n(A∩B)
N(A∩B)=139−n(A∪B)
But n(A∪B)≤100
So, 139−n(A∪B)≥139−100
139−n(A∪B)≥39
n(A∩B)≥39…………(i)
Now,n(A∩B)≤n(A)andn(A∩B)≤n(B)
n(A∩B)≤63andn(A∩B)≤76
n(A∩B)≤63……………(ii)
From Eqs. (i) and (ii),
39≤n(A∩B)≤63
39≤x≤63
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