Question

On behalf of the King , write a notice inviting people to respond to his three question. Mention the question also.​

Answer 1

Answer:

To Find :

% of American who like both i.e. value of x

___________________________

☆ Solution :

Let A and B denote the set of Americans who like Cheese and Apple respectively.

n(A) = 63 and n(B) = 76

According to De-Morgan's Law

n(A U B ) = n(A) + n(B) - n(A∩B)

⟹ n(A U B ) = 63 + 76 - n(A ∩ B)

⟹ n(A ∩ B) = 139 - n(A U B)

But, n(A U B) ⩽ 100

⟹ -n(A U B) ⩾ -100

⟹ 139 - n(A U B) ⩾ 139 - 100 = 39

⟹ 39 ⩽ n(A ∩ B) . . . (i)

Again ,

A ∩ B ⊆ A and A ∩ B ⊆ B

∴ n(A ∩ B) ⩽ n(A) = 63

and n(A ∩ B) ⩽ n(B) = 76

∴ n(A ∩ B) ⩽ 63 . . . (ii)

Combining eq (i) And (ii)

39 ⩽ n(A ∩ B) ⩽ 63

\red{ \huge\underline{\boxed{ \bf 39 \leqslant x \leqslant 63} }}

39⩽x⩽63

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